传统和高阶滑模控制研究及其应用
|
摘要
不确定性条件下的控制问题是现代控制中的一个重要课题,因为在任何控制问题中,实际的控制对象和用于控制器设计的数学模型总是存在差异,这种差异主要来自于外界干扰、未知的对象参数和未建模动态。作为现代控制理论的一个重要分支,滑模控制以实现简单以及系统处于滑动模态时对满足匹配条件的外界干扰、模型的不确定性和未建模动态具有不变性而著称,且已成功应用于机器人、航空航天等领域。
论文研究了传统滑模和高阶滑模控制问题,并将部分研究成果应用于机器人和飞行器的控制中。主要研究内容和创新点如下:
(1)研究了传统滑模控制中采用Slotine形式的滑模面和积分滑模面,利用边界层和幂次趋近律来抑制抖振时,系统的稳态跟踪误差界问题。利用有界输入有界输出(BIBO)稳定的方法,推导出了比现有文献的结果更为精确的稳态跟踪误差界。进一步,通过给定的稳态跟踪误差要求,可以设计合适的边界层厚度或幂次趋近律参数,不用通过仿真实验来试凑。最后,所得到的结果应用到n关节机械臂的跟踪控制中。
(2)为了减小稳态跟踪误差,不少学者将积分项引入到滑模面的设计中。然而,在大的初始误差条件下,积分会出现累积效应(Windup),引起大的超调和执行器饱和,甚至导致系统不稳定。因此,提出了一类具有“小误差放大,大误差饱和”功能的光滑非线性饱和函数以改进传统积分滑模控制,在保持传统积分滑模控制跟踪精度的同时获得更好的暂态性能。应用Lyapunov稳定性理论和LaSalle不变性原理证明了对常值或最终常值干扰可以完全抑制。并在此基础上提出了全程非线性积分滑模控制方法,消除了滑模的到达阶段,具有全程鲁棒性。
(3)基于非光滑的类二次型Lyapunov函数,对二阶滑模Super-Twisting算法的有限时间收敛性进行了分析。系统受常值干扰时,通过Lyapunov方程证明了该算法有限时间收敛,并给出了收敛时间的最优估计;系统受时变干扰时,通过求解代数Riccati方程得出了一组保证该算法有限时间收敛的参数取值范围,并给出了收敛时间的估计值。同时,在此基础上提出自适应Super-Twisting算法,该算法不需要知道不确定性变化率的界。
(4)证明了幂次趋近律本质上是二阶滑模,且趋近过程品质较好,但鲁棒性差。因此,设计了非齐次干扰观测器和快速幂次趋近律相结合的二阶滑模算法,这种二阶滑模算法适用于相对阶为1的系统。经与Shtessel在Automatica上提出的光滑二阶滑模算法进行比较,本算法具有更好的暂态性能。将该算法应用于一类无尾飞行器的姿态控制中,仿真结果表明了该算法的有效性。
(5)利用有限时间控制技术中的齐次理论,并结合自适应控制思想,提出了一种鲁棒自适应二阶滑模控制方法,不需要知道系统不确定性的界。并设计了一类新的非线性函数替代齐次系统中的幂函数,克服了齐次系统在状态远离平衡点时收敛速度慢的缺陷,系统的状态能快速有限时间收敛。该算法形式简单,控制律的设计只需要系统的相对阶信息,并将其应用于Nubot全向移动机器人的轨迹跟踪控制中。
(6)基于齐次理论和有限时间快速收敛Lyapunov函数,提出了鲁棒自适应任意阶滑模控制方法。将SISO系统的r阶滑模控制问题转化为受扰动的r重积分链的有限时间镇定问题,依据第七章的思路,将控制律的设计分成两个部分:名义控制部分和补偿控制部分。名义控制部分分别采用齐次理论和快速有限时间Lyapunov稳定性理论进行设计,补偿控制部分采用自适应一阶滑模方法,综合得到了鲁棒自适应任意阶滑模控制律,并应用于轮式移动机器人的控制中。
Control in the presence of uncertainty is one of the main topics of modern control theory. In the formulation of any control problem there is always a discrepancy between the actual plant dynamics and its mathematical model used for the controller design. These discrepancies mostly come from external disturbances, unknown plant parameters, and unmodeled dynamics. Sliding mode control (SMC), one of the most significant branches in modern control theory, turns out to be characterized by high simplicity and invariance property which lies in its insensitivity to matched uncertainties when in the sliding mode. Thus, it has been widely implemented in many real systems such as robots, aeronautical and space vehicles.
Traditional and higher order sliding mode (HOSM) control are investigated, and partial achievements are applied to robots and aircraft control. The main research contents and contributions are listed as follows:
(1) For the traditional sliding mode tracking control of a class of uncertain nonlinear systems using boundary layer or power reaching rate law to suppress chattering, the steady-state error bounds are studied when use Slotine form sliding surface and integral sliding surface, respectively. Using the method of BIBO stability, the steady-state error bounds are obtained. Compared with the results reported in literatures, the steady-state error bounds in this dissertation is more accurate. Furthermore, by specifying the tracking error that is required, an appropriate saturation function or power reaching law to suppress chattering is designed without simulation experiments. A case study of an n-link robot manipulator model is presented to demonstrate the effectiveness of the analysis.
(2) In order to decrease the steady-state error, many scholars introduced integral term in the sliding surface design. However, with the existence of large initial error, integrator windup would occur and give rise to overshoots and even lead to instability. Therefore, to promote the performance of traditional integral sliding mode control, a new nonlinear saturation function is proposed, which enhances small errors and be saturated with large errors in shaping the tracking errors. While maintaining the tracking accuracy of the traditional integral sliding mode control, this approach provides better transient performances. Using Lyapunov stability theory and LaSalle invariance principle, we proved that the proposed approach ensures the zero steady-state error in the presence of a constant disturbance or an asymptotically constant disturbance. Furthermore, global nonlinear integral sliding mode control is proposed to provide a framework for eliminating the reaching phase, so that a sliding mode exists throughout the entire response.
(3) The finite time convergence of the second order sliding Super-Twisting algorithm is analyzed using a non-smooth quadratic-like Lyapunov function. For the constant disturbance, the finite time convergence is proved through Lyapunov equation, and the optimal estimation of the convergence time is presented. For the time varying disturbance, the finite time convergence of Super-Twisting is guaranteed when the parameters satisfy the algebraic Riccati equation, and the estimation of the convergence time is provided. Finally, based on the non-smooth quadratic-like Lyapunov function, adaptive Super-Twisting algorithm is proposed that continuously drives the sliding variable and its derivative to zero in the presence of the disturbance with the unknown bounded variation.
(4) It is proved that power rate reaching law, in essential, is second order sliding mode which has perfect reaching quality but poor robustness. Therefore, a robust second order sliding mode control scheme for first order dynamic systems is proposed. The controller has finite time convergent property and contains two parts. A part is fast power reaching law which is used to stabilize sliding variable and its derivative to zero in finite time without disturbance. The other part is a non-homogeneous disturbance observer, which can provide for exact estimation of the sufficiently smooth disturbance in finite time. As a result, a continuous second order sliding mode is established in finite time. Compared our method with the smooth second order sliding mode proposed by Shtessel in the Automatica, a better transient performance is obtained by our method. Simulation results using a tailless aircraft model show good performance even in actuator failure scenarios which validates the effectiveness and feasibility of the proposed method.
(5) Using homogeneity and adaptive sliding mode concept, a robust adaptive second order sliding mode control scheme is proposed, and the bounds of uncertainties are not required to be known in advance. Power function in the homogeneous system is replaced by a proposed nonlinear function, thus, a fast convergence rate is guaranteed for any distance from equilibrium point. The convergence rate of the second order sliding mode can be hastened through tuning the controller parameters, and the robustness is ensured. The method is evaluated in simulations on an Omni-directional Mobile Robot (Nubot).
(6) Based on homogeneity and finite-time convergent Lyapunov function, a robust adaptive arbitrary order sliding mode control method is proposed. It is shown that the problem is equivalent to the finite time stabilization problem for a perturbed chain of integrators. The control law contains two parts: the nominal part, which is designed using homogeneity technique and finite-time Lyapunov stability theory, respectively, achieves finite time stabilization of the chain of integrators without uncertainties; the compensating part, which is designed using adaptive sliding mode, rejects bounded uncertainties, and the bounds of uncertainties are not required to be known in advance. As a result, a finite time convergent arbitrary order sliding mode is established. An illustrative example of a wheeled mobile robots control shows the applicability of the method.
论文研究了传统滑模和高阶滑模控制问题,并将部分研究成果应用于机器人和飞行器的控制中。主要研究内容和创新点如下:
(1)研究了传统滑模控制中采用Slotine形式的滑模面和积分滑模面,利用边界层和幂次趋近律来抑制抖振时,系统的稳态跟踪误差界问题。利用有界输入有界输出(BIBO)稳定的方法,推导出了比现有文献的结果更为精确的稳态跟踪误差界。进一步,通过给定的稳态跟踪误差要求,可以设计合适的边界层厚度或幂次趋近律参数,不用通过仿真实验来试凑。最后,所得到的结果应用到n关节机械臂的跟踪控制中。
(2)为了减小稳态跟踪误差,不少学者将积分项引入到滑模面的设计中。然而,在大的初始误差条件下,积分会出现累积效应(Windup),引起大的超调和执行器饱和,甚至导致系统不稳定。因此,提出了一类具有“小误差放大,大误差饱和”功能的光滑非线性饱和函数以改进传统积分滑模控制,在保持传统积分滑模控制跟踪精度的同时获得更好的暂态性能。应用Lyapunov稳定性理论和LaSalle不变性原理证明了对常值或最终常值干扰可以完全抑制。并在此基础上提出了全程非线性积分滑模控制方法,消除了滑模的到达阶段,具有全程鲁棒性。
(3)基于非光滑的类二次型Lyapunov函数,对二阶滑模Super-Twisting算法的有限时间收敛性进行了分析。系统受常值干扰时,通过Lyapunov方程证明了该算法有限时间收敛,并给出了收敛时间的最优估计;系统受时变干扰时,通过求解代数Riccati方程得出了一组保证该算法有限时间收敛的参数取值范围,并给出了收敛时间的估计值。同时,在此基础上提出自适应Super-Twisting算法,该算法不需要知道不确定性变化率的界。
(4)证明了幂次趋近律本质上是二阶滑模,且趋近过程品质较好,但鲁棒性差。因此,设计了非齐次干扰观测器和快速幂次趋近律相结合的二阶滑模算法,这种二阶滑模算法适用于相对阶为1的系统。经与Shtessel在Automatica上提出的光滑二阶滑模算法进行比较,本算法具有更好的暂态性能。将该算法应用于一类无尾飞行器的姿态控制中,仿真结果表明了该算法的有效性。
(5)利用有限时间控制技术中的齐次理论,并结合自适应控制思想,提出了一种鲁棒自适应二阶滑模控制方法,不需要知道系统不确定性的界。并设计了一类新的非线性函数替代齐次系统中的幂函数,克服了齐次系统在状态远离平衡点时收敛速度慢的缺陷,系统的状态能快速有限时间收敛。该算法形式简单,控制律的设计只需要系统的相对阶信息,并将其应用于Nubot全向移动机器人的轨迹跟踪控制中。
(6)基于齐次理论和有限时间快速收敛Lyapunov函数,提出了鲁棒自适应任意阶滑模控制方法。将SISO系统的r阶滑模控制问题转化为受扰动的r重积分链的有限时间镇定问题,依据第七章的思路,将控制律的设计分成两个部分:名义控制部分和补偿控制部分。名义控制部分分别采用齐次理论和快速有限时间Lyapunov稳定性理论进行设计,补偿控制部分采用自适应一阶滑模方法,综合得到了鲁棒自适应任意阶滑模控制律,并应用于轮式移动机器人的控制中。
Control in the presence of uncertainty is one of the main topics of modern control theory. In the formulation of any control problem there is always a discrepancy between the actual plant dynamics and its mathematical model used for the controller design. These discrepancies mostly come from external disturbances, unknown plant parameters, and unmodeled dynamics. Sliding mode control (SMC), one of the most significant branches in modern control theory, turns out to be characterized by high simplicity and invariance property which lies in its insensitivity to matched uncertainties when in the sliding mode. Thus, it has been widely implemented in many real systems such as robots, aeronautical and space vehicles.
Traditional and higher order sliding mode (HOSM) control are investigated, and partial achievements are applied to robots and aircraft control. The main research contents and contributions are listed as follows:
(1) For the traditional sliding mode tracking control of a class of uncertain nonlinear systems using boundary layer or power reaching rate law to suppress chattering, the steady-state error bounds are studied when use Slotine form sliding surface and integral sliding surface, respectively. Using the method of BIBO stability, the steady-state error bounds are obtained. Compared with the results reported in literatures, the steady-state error bounds in this dissertation is more accurate. Furthermore, by specifying the tracking error that is required, an appropriate saturation function or power reaching law to suppress chattering is designed without simulation experiments. A case study of an n-link robot manipulator model is presented to demonstrate the effectiveness of the analysis.
(2) In order to decrease the steady-state error, many scholars introduced integral term in the sliding surface design. However, with the existence of large initial error, integrator windup would occur and give rise to overshoots and even lead to instability. Therefore, to promote the performance of traditional integral sliding mode control, a new nonlinear saturation function is proposed, which enhances small errors and be saturated with large errors in shaping the tracking errors. While maintaining the tracking accuracy of the traditional integral sliding mode control, this approach provides better transient performances. Using Lyapunov stability theory and LaSalle invariance principle, we proved that the proposed approach ensures the zero steady-state error in the presence of a constant disturbance or an asymptotically constant disturbance. Furthermore, global nonlinear integral sliding mode control is proposed to provide a framework for eliminating the reaching phase, so that a sliding mode exists throughout the entire response.
(3) The finite time convergence of the second order sliding Super-Twisting algorithm is analyzed using a non-smooth quadratic-like Lyapunov function. For the constant disturbance, the finite time convergence is proved through Lyapunov equation, and the optimal estimation of the convergence time is presented. For the time varying disturbance, the finite time convergence of Super-Twisting is guaranteed when the parameters satisfy the algebraic Riccati equation, and the estimation of the convergence time is provided. Finally, based on the non-smooth quadratic-like Lyapunov function, adaptive Super-Twisting algorithm is proposed that continuously drives the sliding variable and its derivative to zero in the presence of the disturbance with the unknown bounded variation.
(4) It is proved that power rate reaching law, in essential, is second order sliding mode which has perfect reaching quality but poor robustness. Therefore, a robust second order sliding mode control scheme for first order dynamic systems is proposed. The controller has finite time convergent property and contains two parts. A part is fast power reaching law which is used to stabilize sliding variable and its derivative to zero in finite time without disturbance. The other part is a non-homogeneous disturbance observer, which can provide for exact estimation of the sufficiently smooth disturbance in finite time. As a result, a continuous second order sliding mode is established in finite time. Compared our method with the smooth second order sliding mode proposed by Shtessel in the Automatica, a better transient performance is obtained by our method. Simulation results using a tailless aircraft model show good performance even in actuator failure scenarios which validates the effectiveness and feasibility of the proposed method.
(5) Using homogeneity and adaptive sliding mode concept, a robust adaptive second order sliding mode control scheme is proposed, and the bounds of uncertainties are not required to be known in advance. Power function in the homogeneous system is replaced by a proposed nonlinear function, thus, a fast convergence rate is guaranteed for any distance from equilibrium point. The convergence rate of the second order sliding mode can be hastened through tuning the controller parameters, and the robustness is ensured. The method is evaluated in simulations on an Omni-directional Mobile Robot (Nubot).
(6) Based on homogeneity and finite-time convergent Lyapunov function, a robust adaptive arbitrary order sliding mode control method is proposed. It is shown that the problem is equivalent to the finite time stabilization problem for a perturbed chain of integrators. The control law contains two parts: the nominal part, which is designed using homogeneity technique and finite-time Lyapunov stability theory, respectively, achieves finite time stabilization of the chain of integrators without uncertainties; the compensating part, which is designed using adaptive sliding mode, rejects bounded uncertainties, and the bounds of uncertainties are not required to be known in advance. As a result, a finite time convergent arbitrary order sliding mode is established. An illustrative example of a wheeled mobile robots control shows the applicability of the method.
引文
[1] Astrom K J, Wittenmark B. Adaptive Control [M]. Addison-Wesley, 1995.
[2] Camacho E F, Bordons C. Model Predictive Control [M]. Berlin: Speinger-Verlag, 2004.
[3] Krstic M, Kanellakopoulos I, Kokotovic P. Nonlinear and Adaptive Control Design [M]. New York: Wiley, 1995.
[4] Utkin V. Sliding Mode in Control and Optimization [M]. Berlin: Springer-Verlag, 1992.
[5] Draznenovic B.The Invariance Conditions in Variable Structure Control Systems [J].Automatica, 1969, 5(2): 287-295.
[6] Isidori A. Nonlinear Control Systems [M]. Berlin: Springer-Verlag, 1995.
[7]张文修,梁广锡.模糊控制与系统[M].西安:西安交通大学出版社, 1998.
[8] Emel'yanov S V, Taran V A. On a Class of Variable Structure Control Systems. In: USSR Academy of Sciences, Energy and Automation. Moskov, 1962. (in Russian)
[9] Emel'yanov S V. Theory of Variable Structure Systems [M]. Moscow: Nauke, 1970.
[10] Utkin V I. Sliding Modes and Their Application in Variable Structure Systems [M]. Moscow: Nauka, 1970. (in Russian).
[11] Itkis U. Control Systems of Variable Structure [M]. New York: Wiley, 1976.
[12] Utkin V I. Variable Structure Systems with Sliding Modes [J]. IEEE Transactions on Automatic Control, 1977, 22(2), 212-222.
[13] Pan S, Su H, Hu X, Chu J. Variable Structure Control Theory and Application: A Suvery [C]//Proceedings of the 3rd World Congress on Intelligent Control and Automation, Heifei, P.R.China, 2000: 2977-2981.
[14]高为炳.变结构控制理论基础[M].北京:中国科学技术出版社, 1990.
[15]胡跃明,周其节.分布参数变结构控制系统[M].北京:国防工业出版社, 1996.
[16]姚琼荟,黄继起,吴汉松.变结构控制系统[M].重庆:重庆大学出版社, 1997.
[17]胡跃明.变结构控制理论与应用[M].北京:科学出版社, 2003.
[18]刘金琨.滑模变结构控制Matlab仿真[M].北京:清华大学出版社, 2005.
[19]傅春,谢剑英.模糊滑模控制研究综述[J].信息与控制, 2001, 30(5): 434-440.
[20]张晓宇,苏宏业.滑模变结构控制理论进展综述[J].化工自动化及仪表. 2006, 33(2): 1-8.
[21]刘金琨,孙富春.滑模变结构控制理论及其算法研究与进展[J].控制理论与应用, 2007, 24(3): 407-419.
[22] Yu X, Kaynak O. Sliding-Mode Control with Soft Computing: A Survey [J]. IEEETransactions on Industrial Electronics, 2009, 56(9): 3275-3285.
[23] Young K D, Utkin V I, Ozguner U. A Control Engineer’s Guide to Sliding Mode Control [J]. IEEE Transaction on Control Systems Technology, 1999, 7(3): 328-342.
[24] Slotine J J E, Sastry S S. Tracking Control of Nonlinear Systems using Sliding Surfaces with Application to Robot Manipulator [J]. International Journal of Control, 1983, 38(2): 465-492.
[25] Slotine J J E. Sliding Controller Design for Non-linear Systems [J]. International Journal of Control, 1984, 40(2): 421-434.
[26] Chen M S, Hwang Y R, Tomizuka M. A State-Dependent Boundary Layer Design for Sliding Mode Control [J]. IEEE Transaction on Automatic Control, 2002, 47(10): 1677-1681.
[27] Chen M S, Hwang Y R, Tomizuka M. Sliding Mode Control Reduced Chattering For Systems With Dependent Uncertainties [C]//Proceedings of the 2004 IEEE International Conference on Networking, Sensing & Control, Taipei, Taiwan, 2004: 967-971.
[28] Lee H, Kim E, Kang H J, Park M. A New Sliding-Mode Control with Fuzzy Boundary Layer [J], Fuzzy Sets and Systems, 2001, 120(1): 135-143.
[29] Cupertino F, Naso D, Mininno E, Turchiano B. Sliding-Mode Control with Double Boundary Layer for Robust Compensation of Payload Mass and Friction in Linear Motors [J]. IEEE Transactions on Industry Applications, 2009, 45(5): 1688-1696.
[30] Benayache R, Chrifi-Alaoui L, Bussy P, Castelain J M. Design and Implementation of Sliding Mode Controller with Varying Boundary Layer for a Coupled Tanks Systems[C]//17th Mediterranean Conference on Control & Application, Thessaloniki, Greece, 2009: 1215-1220.
[31] Gao W, Hung J C, Variable Structure Control of Nonlinear Systems: A New Approach [J]. IEEE Transactions on Industrial Electronics, 1993, 40(1): 45-55.
[32]李文林,李巧萍.可抑制抖振的滑动模态到达条件[C]//Proceedings of the 27th Chinese Control Conference, Kunming, China, 2008: 154-158.
[33] Yu S, Yu X, Shirinzadeh B, Man Z. Continuous Finite-Time Control for Robotic Manipulators with Terminal Sliding Mode [J]. Automatica, 2005, 41(11): 1957-1964.
[34]梅红,王勇.快速收敛的机器人滑模变结构控制[J].信息与控制, 2009, 38(5): 522-558.
[35] Tsai C H, Chung H Y, Yu F M. Neural-Sliding Mode Control with Its Applications in Seesaw Systems [J]. IEEE Transactions on Neural Networks, 2004, 15(1): 124-134.
[36] Fang Y, Chow T W S, Li X D. Use of a Recurrent Neural Network in DiscreteSliding-Mode Control [J]. IEE Control Theory and Applications, 1999, 146(1): 84-90.
[37]刘殿通,易建强,谭民.一类非线性系统的自适应滑模模糊控制[J].自动化学报, 2004, 30(1): 143-150.
[38] Hwang Y R, Tomizuka M. Fuzzy Smoothing Algorithms for Variable Structure Systems [J]. IEEE Transactions on Fuzzy Systems, 1994, 2(4): 277-284.
[39] Wu J, Ham T S. A Sliding-Mode Approach to Fuzzy Control Design [J], IEEE Transaction on Control Systems Technology, 1996, 4(2): 141-151.
[40] Wai R J. Adaptive Fuzzy Sliding-Mode Control for Electrical Servo Drive [J]. IEEE Transaction on Industry Electronic, 2007, 54(1): 586-594.
[41] Sadati N, Ghadami R. Adaptive Multi-Model Sliding Mode Control of Robotic Manipulators using Soft Computing [J]. Neurocomputing, 2008, 71(2): 2702-2710.
[42]张金萍,刘阔,林剑锋,马晓波,于文东.挖掘机的4自由度自适应模糊滑模控制[J].机械工程学报, 2010, 46(21): 87-92.
[43] Lin S C, Chen Y Y. Design of Self-Learning Fuzzy Sliding Mode Controllers Based on Genetic Algorithm [J]. Fuzzy Sets Systems, 1997, 86(2): 139-153.
[44] Xu J X, Lee T H, Wang M, Yu X H. Design of Variable Structure Controllers with Continuous Switching Control [J]. International Journal of Control, 1996, 65(3): 409-431.
[45] Furuta K, Pan Y. Sliding Sectors for VS Controller [J]. Automatica, 2000, 36(2): 211-228.
[46] Pan Y, Kumar D, Liu G, Furuta K. Design of Variable Structure Control System with Nonlinear Time-Varying Sliding Sector [J]. IEEE Transactions on Automatic Control, 2009, 54(8): 1981-1986.
[47] Kang B P, Ju J L. Sliding Mode Controller with Filtered Signal for Robot Manipulators using Virtual Plant/Controller [J]. Mechatronics, 1997, 7(3): 277-286.
[48] Yanada H, Ohnishi H. Frequency-Shaped Sliding Mode Control of an Electrohydraulic Servomotor [J]. Journal of Systems and Control and Dynamics, 1991, 213(1): 441-448.
[49] Korondi P, Young D, Hashimoto H. Sliding Mode Based Disturbance Observer for Motion Control [C]//Proceedings of the 37th IEEE Conference on Decision and Control, Florida, USA, 1998: 1926-1927.
[50] Eun Y, Kim J H, Kim K, Cho D H. Discrete-Time Variable Structure Controller with a Decoupled Disturbance Compensator and Its Applications to a CNC Servomechanism [J]. IEEE Transactions on Control Systems Technology, 1999, 7(4): 414-422.
[51]宋立忠,陈少昌,姚琼荟.多输入不确定系统离散变结构控制设计[J].控制与决策, 2003, 18(4): 468-471.
[52] Koshkouei A J, Burnham K J, Zinober A S I. Dynamic Sliding Mode Control Design [J]. IEE Proceedings - Control Theory and Applications, 2005, 152(4): 392-396.
[53] Bregeault V, Plestan F, Shtessel Y B, Poznyak A. Adaptive Sliding Mode Control for an Electropneumatic Actuator [C] // Proceedings of 2010 11th International Workshop on Variable Structure Systems, Mexico City, Mexico, 2010: 260-265.
[54] Yoo D S, Chung M J. A Variable Structure Control with Simple Adaptation Laws for Upper Bounds on the Norm of the Uncertainties [J]. IEEE Transaction on Automatic Control, 1992, 37(6): 860-865.
[55] Su C Y, Leung T P. A Sliding Mode Controller with Bound Estimation for Robot Manipulators [J]. IEEE Transaction on Robotics and Automation, 1993, 9(2): 208-214.
[56] Wheeler G, Su C Y, Stepanenko Y. A Sliding Mode Controller with Improved Adaptation Laws for the Upper Bounds on the Norm of Uncertainties [J]. Automatica, 34(2): 1657-1661.
[57] Munoz D, Sbarbaro D. An Adaptive Sliding Mode Controller for Discrete Nonlinear Systems [J]. IEEE Transactions on Industrial Electronics, 2000, 47(3): 574-581.
[58] Tao C W, Chan M L, Lee T T. Adaptive Fuzzy Sliding Mode Controller for Linear Systems with Mismatched Time-Varying Uncertainties [J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, 2003, 33(2): 283-294.
[59] Lin F J, Chiu S L. Novel Sliding Mode Controller for Synchronous Motor Drive [J]. IEEE Transactions on Aerospace and Electronic Systems, 1998, 34(2): 532-542.
[60] Lin F J, Chou W D, Huang P K. Adaptive Sliding-Mode Controller Based on Real-Time Genetic Algorithm for Induction Motor Servo Drive [J]. IEE Proceedings B Electric Power Applications, 2003, 150(1): 1-13.
[61] Huang Y J, Kuo T C, Chang S H. Adaptive Sliding-Mode Control for Nonlinear Systems with Uncertain Parameters [J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, 2008, 38(2): 534-539.
[62] Plestan F, Shtessel Y B, Bregeault V, Poznyak A. New Methodologies for Adaptive Sliding Mode Control [J]. International Journal of Control, 2010, 83(9): 1907-1919.
[63] Lee H, Utkin V I. Chattering Suppression Methods in Sliding Mode Control Systems [J]. Annual Reviews in Control, 2007, 31(2): 179-188.
[64] Ambrosino G, Celektano G, Garofalo F. Variable Structure Model Reference Adaptive Control Systems [J]. International Journal of Control, 1984, 39(6): 1139-1349.
[65] Liu H. Variable Structure Model-Reference Adaptive Control (VS-MRAC) Using Only Input and Output Measurements: The General Case [J]. IEEE Transactions on Automatic Control, 1990, 35(11): 1238-1243.
[66] Liu H. Lizarralde F, DeAraujo A D. New Results on Output-Feedback Variable Structure Model-Reference Adaptive Control: Design and Stability Analysis [J]. IEEE Transactions on Automatic Control, 1997, 42(3): 1-7.
[67]林岩,毛剑琴,操云甫.鲁棒低增益变结构模型参考自适应控制[J].自动化学报, 2001, 27(5): 665-671.
[68]张达科,胡跃明,吴捷,郭华芳.类反斜线回滞系统的模型参考滑模控制[J].控制理论与应用, 2005, 22(3): 402-407.
[69] Khalil H K. Nonlinear Systems [M], 3rd Ed, Upper Saddle River, New Jersey:Prentice-Hall, 2002.
[70] Chern T L, Wu Y C. Design of Integral Variable Structrue Controller and Application to Electrohydraulic Velocity Servosystems [J]. IEE Proceedings D Control Theory and Applications, 1991, 138(5): 439-444.
[71] Chern T L, Wu Y C. Integral Variable Structure Control Approach for Robot Manipulators [J], IEE Proceedings D Control Theory and Applications, 1992, 139(2): 161-166.
[72] Chern T L, Wu Y C. Design of Brushless DC Position Servo Systems using Integral Variable Structure Approach [J]. IEE Proceedings B Electric Power Applications, 1993, 140(1): 27-34.
[73] Chern T L, Chang J, Chang G K. DSP-Based Integral Variable Structure Model Following Control for Brushless DC Motor Drivers [J]. IEEE Transactions on Power Electronics, 1997, 12(1): 53-63.
[74] Wang J D, Lee T L, Juang Y T. New Methods to Design an Integral Variable Structure Controller [J]. IEEE Transactions on Automatic Control, 1996, 41(1): 140-143.
[75] Lee J H, Allaire P E, Tao G, Zhang X. Integral Sliding-Mode Control of a Magnetically Suspended Balance Beam: Analysis, Simulation, and Experiment. IEEE/ASME Transactions on Mechatronics, 2001, 6(3): 338-346.
[76] Slotine J J. Li W P. Applied Nonlinear Control [M]. New Jersey: Prentice-Hall, 1991.
[77] Bouri M, Thomasset D. Sliding Control of an Electropneumatic Actuator Using an Integral Switching Surface [J]. IEEE Transactions on Control Systems Technology, 2001, 9(2): 368-375.
[78]张天平,梅建东,沈启坤.具有模糊监督控制器的积分变结构间接自适应控制[J].控制理论与应用, 2007, 24(1): 90-95.
[79]管成,潘双夏.含有非线性不确定参数的电液系统滑模自适应控制[J].控制理论与应用, 2008, 25(2): 261-267.
[80] Hung C P. Integral Variable Structure Control of Nonlinear System Using a CMAC Neural Network Learning Approach [J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, 2004, 34(1): 702-709.
[81] Stepanenko Y, Cao Y, Su C. Variable Structure Control of Robotic Manipulator with PID Sliding Surfaces [J]. International Journal of Robust and Nonlinear Control, 1998, 8(1): 79-90.
[82] Parra-Vega V, Arimoto S, Liu Y H, Hirzinger G, Akella P. Dynamic Sliding PID Control for Tracking of Robot Manipulators: Theory and Experiments [J]. IEEE Transactions on Robotics and Automation, 2003, 19(6): 967-976.
[83] Eker I. Sliding Mode Control with PID Sliding Surface and Experimental Application to an Electromechanical Plant [J]. ISA Transactions, 2006, 45(1): 109-118.
[84]王敏,杜克林,黄心汉.机器人滑模轨迹跟踪控制[J].机器人, 2001, 23(3): 217-222.
[85] Utkin V, Shi J. Integral Sliding Mode in Systems Operating under Uncertainty Conditions [C]//Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan, 1996: 4591-4596.
[86] Yahaya M S, Johari O, Ruddin A G. A Class of Proportional-Integral Sliding Mode Control with Application to Active Suspension System [J]. Systems & Control Letters, 2004, 51(3/4): 217-223.
[87] Niu Y, Daniel W C, Lam J. Robust Integral Sliding Mode Control for Uncertain Stochastic Systems with Time-Varying Delay [J]. Automatica, 2005, 41(5): 873-880.
[88] Comanescu M, Xu L, Batzel T D. Decoupled Current Control of Sensorless Induction-Motor Drives by Integral Sliding Mode [J]. IEEE Transactions on Industrial Electronics, 2008, 55(11): 3836-3845.
[89] Seshagiri S, Khalil H K. On introducing Integral Action in Sliding Mode Control [C]//Proceedings of the 41st IEEE Conference on Decision and Control, Nevada, USA, 2002: 1473-1478.
[90] Levant A. Sliding Order and Sliding Accuracy in Sliding Mode Control [J]. International Journal of Control, 1993, 58(6): 1247-1263.
[91] Levantovsky L V (Levant A). Higher Order Sliding Modes and Their Application for Controlling Uncertain Processes [D]. Ph.D. Dissertation, Institute for system studies of the USSR Academy of Science, Moscow, 1987.
[92] Fridman L, Levant A. Higher order Sliding Modes as the Natural Phenomena of Control Theory [C] //Proceedings of the Workshop Variable Structure and Lyapunov Technique, Benevento, 1994: 302-309.
[93] Bartolini G, Pisano A, Punta E, Usai E. A Survey of Application of Second-Order Sliding Mode Control to Mechanical Systems [J]. International Journal of Control, 2003, 76(9/10): 875-982.
[94] Levant A. Robust exact differentiation via Sliding Mode Technique [J]. Automatica, 1998, 34(3): 379-384.
[95] Levant A. Universal SISO Sliding-Mode Controllers with Finite-Tine Convergence [J]. IEEE Transactions on Automatic Control, 2001, 46(9): 1447-1451.
[96] Levant A. Higher Order Sliding Modes, Differentiation and Output-Feedback Control [J]. International Journal of Control, 2003, 76(9/10): 924-941.
[97] Man Z, Paplinski A P, Wu H. A Robust MIMO Terminal Sliding Mode Control for Rigid Robotic Manipulators [J]. IEEE Transactions on Automatic Control, 1994, 39(12): 2464-2468.
[98] Bartolini G, Ferrara, A, Usai, E. Output Tracking Control of Uncertain Nonlinear Second-Order Systems [J]. Automatica, 1997, 33(12): 2203–2212.
[99] Bartolini G, Ferrara A, Usai, E. Chattering Avoidance by Second-Order Sliding Mode Control [J]. IEEE Transactions on Automatic Control, 1998, 43(2): 241-246.
[100] Shtessel Y B, Shkolnikov I A, Brown M J. An Asymptotic Second-Order Smooth Sliding Mode Control [J]. Asian Journal of Control, 2003, 5(4): 498-504.
[101] Shtessel Y B, Shkolnikov I A, Levant A. Smooth Second Modes: Missile Guidance Application [J]. Automatica, 2007, 43(8): 1470-1476.
[102] Shtessel Y B, Tournes C H. Integrated Higher-Order Sliding Mode Guidance and Autopilot for Dual-Control Missiles [J]. AIAA Journal of Guidance, Control, and Dynamics, 2009, 32(1): 79-94.
[103] Shtessel Y B, Shkolnikov I A, Levant A. Guidance and Control of Missile Interceptor using Second-Order Sliding Modes [J]. IEEE Transactions on Aerospace Electronic Systems, 2009, 45(1): 110-123.
[104] Pan Y, Liu G, Kumar K D. Robust Stability Analysis of Asymptotic Second-order Sliding Mode Control System Using Lyapunov Function [C]// Proceeding of the 2010 IEEE International Conference on Information and Automation, Harbin, China, 2010: 313-318.
[105] Plestan F, Moulay E, Glumineau A, Cheviron T. Robust Output Feedback Sampling Control Based on Second-Order Sliding mode [J]. Automatica, 2010, 46(6): 1096-1100.
[106] Plestan F, Glumineau A. A New Differentiator Based on a Second Order Sliding Mode Output Feedback Control [C]//Proceedings of 49th IEEE Conference on Decision and Control, Atlanta, USA, 2010.
[107] Polyakov A, Poznyak A. Lyapunov Function Design for Finite-Time Convergence Analysis:“Twisting”Controller for Second-Order Sliding Mode Realization [J]. Automatica, 2009, 45(2): 444-448.
[108] Polyakov A, Poznyak A. Reaching Time Estimation for“Super-Twisting”Second Order Sliding Mode Controller via Lyapunov Function Designing [J], IEEE Transactions on Automatic Control, 2009, 54(8): 1951-1955.
[109] Jaime A M, Marisol O. A Lyapunov Approach to Second Order Sliding Mode Controllers and Observers [C]//Proceedings of the IEEE International Conference on Decision and Control. New York, USA, 2008: 2856-2861.
[110] Davila A, Jaime A M, Fridman L. Optimal Lyapunov Function Selection for Reaching Time Estimation of Supper Twisting Algorithm[C]//Proceedings of Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference. Shanghai, China, 2009: 8045-8410.
[111] Bartolini G, Pisano A, Usai E. On the Finite-Time Stabilization of Uncertain Nonlinear Systems with Relative Degree Three [J]. IEEE Transactions on Automatic Control, 2007, 52(11): 2134-2141.
[112] Bartolini G, Pillosu S, Pisano A, Usai E. Time-Optimal Stabilization for a Third-Order Integrator: a Robust State-Feedback Implementation [M], in Dynamics, Bifurcations and Control, Lecture Notes in Control and Information Sciences, Springer-Verlag, 2002, 273: 131-144.
[113] Levant A. Quasi-Continuous Higher-Order Sliding-Mode Controllers [J], IEEE Transactions on Automatic Control, 2005, 50(11): 1812-1816.
[114] Levant A, Alelishvili L. Integral High-Order Sliding Modes [J], IEEE Transaction on Automatic Control, 2007, 52(7): 1278-1282.
[115] Laghrouche S, Plestan F, Glumineau A. Practical Higher Order Sliding Mode Control: Optimal Control Based Approach and Application to Electromechanical Systems. In: Edwards, Fossas Colet, & Fridman (Eds.), Advances in Variable Structure and Sliding Mode Control. Lecture Notes in Control and Information Sciences: (vol. 334), Berlin: Springer. 2006.
[116] Laghrouche S, Plestan F, Glumineau A. Higher Order Sliding Mode Control Based on Integral Sliding Mode [J]. Automatica, 2007, 43(3): 531-537.
[117] Plestan F, Glumineau A, Laghrouche S. A New Algorithm for High-Order Sliding Mode Control [J]. International Journal of Robust and Nonlinear Control, 2008, 18(4/5): 441-453.
[118] Defoort M, Floquet T, Kokosy A, Perruquetti W. A Novel Higher Order Sliding Mode Control Scheme [J]. Systems & Control Letter, 2009, 58(2): 102-108.
[119]丁世宏,李世华.有限时间控制问题综述[J].控制与决策, 2011, 26(2): 161-169.
[120] Dinuzzo F, Ferrara A. Higher Order Sliding Mode Controllers with Optimal Reaching [J]. IEEE Transactions on Automatic Control, 2009, 54(9): 2126-2136.
[121] Zong Q, Zhao Z -S, Zhang J. Higher Order Sliding Mode Control with Self-tuningLaw Based on Integral Sliding Mode [J]. IET Control Theory and Applications, 2010, 4(7): 1282-1289.
[122]陈杰,李志平,张国柱.不确定非线性系统的高阶滑模控制器设计[J].控制理论与应用,2010, 27(5): 563-570.
[123] Brierley S D, Longchamp R. Application of Sliding-Mode Control to Air-Air Interception Problem [J]. IEEE Transaction on Aerospace and Electronic Systems, 1990, 26(2): 306-325.
[124] Zhou D, Mu C D, Xu W L. Adaptive Sliding-Mode Guidance of a Homing Missile [J]. AIAA Journal of Guidance, Control, and Dynamics, 1999, 22(4): 589-594.
[125]孙未蒙,郑志强.一种多约束条件下的三维变结构制导律[J].宇航学报, 2007, 28(2): 344-349.
[126]周军,王婷.基于二阶滑模控制的驾束制导导弹一体化制导系统设计[J].宇航学报,2007, 28(6): 1632-1637.
[127] Shtessel Y B, Shkolnikov I A. Aeronautical and Space Vehicle Control in Dynamic Sliding Manifolds [J]. International Journal of Control, 2003, 76(9/10): 1000-1017.
[128] Pukdeboon C, Zinober A S I, Thein M–W. Quasi-Continuous Higher Order Sliding-Mode Controllers for Spacecraft-Attitude-Tracking Maneuvers [J], IEEE Transaction on Industrial Electronics, 2010, 57(4): 1436-1444.
[129] Hall C, Shtessel Y B. Sliding Mode Disturbance Observers-based Control for a Reusable Launch Vehicle [J]. AIAA Journal on Guidance, Control, and Dynamics, 2006, 29(6): 1315-1329.
[130] Shtessel Y B, Buffington J, Banda S. Tailless Aircraft Flight Control Using Multiple Time Scale Re-configurable Sliding Modes [J]. IEEE Transactions on Control Systems Technology, 2002, 10(2): 288-296.
[131] Massey T, Shtessel Y B. Continuous Traditional and High Order Sliding Modes for Satellite Formation Control [J]. AIAA Journal on Guidance, Control, and Dynamics, 2005, 28(4): 826-831.
[132] Haerlian F, Achour K, Floquet T, Perruquetti W. Higher Order Sliding Mode Control of Wheeled Mobile Robots in the Presence of Sliding Effects [C]// Proceeding of the 44th IEEE Conference on Decision and Control, and European Control Conference, Seville, Spain, 2005: 1959-1963.
[133] Lee S U, Chang P H. Control of a Heavy-Duty Robotic Excavator using Time Delay Control with Integral Sliding Surface [J]. Control Engineering Practice, 2002, 10(7) : 679-711.
[134] Ferrara A, Magnani L. Motion Control of Rigid Robot Manipulators via First and Second Order Sliding Modes [J]. Journal of Intelligent Robot Systems, 2007, 48(1):23-36.
[135]胡跃明,晁红敏,李志权,梁天培.非线性仿射控制系统的高阶滑模控制[J].自动化学报, 2002, 28(3): 1-6.
[136] Butt Q R, Bhatti A I. Estimation of Gasoline-Engine Parameters Using Higher Order Sliding Mode [J]. IEEE Transactions on Industrial Electronics, 2008, 55(11): 3891-3898.
[137] Yagiz N, Hacioglu Y, Taskin Y. Fuzzy Sliding-Mode Control of Active Suspensions [J]. IEEE Transactions on Industrial Electronics, 2008, 55(11): 3883-3890.
[138] Pisano A, Usai E. Output-Feedback Control of an Underwater Vehilce Prototype by Higher-Order Sliding Modes [J]. Automatica, 2004, 40(9): 1525-1531.
[139] Bartolini G, Pisano A. Black-Box Position and Attitude Tracking for Underwater Vehicles by Second-Order Sliding-Mode Technique [J]. International Journal of Robust and Nonlinear Control. 2010, 20(14): 1594-1609.
[140] Ignaciuk P, Bartoszewicz A. Sliding-Mode Controller for Connection-Oriented Communication Networks [J]. IEEE Transactions on Industrial Electronics, 2008, 55(11): 4013-4021.
[141] Pan Y, Ozguner U, Dagci O H. Variable-Structure Control of Electronic Throttle Valve [J]. IEEE Transactions on Industrial Electronics, 2008, 55(11): 3899-3907.
[142]王江,曾启明.基于奇异摄动方法的同步电机二阶滑模控制器的设计[J].中国电机工程学报, 2003, 23(10): 142-148.
[143]孙宜标,杨雪,夏加宽.采用鲁棒微分器的永磁直线同步电机二阶滑模控制[J].中国电机工程学报, 2007, 27(33): 6-11.
[144]刘贤兴,胡育文,卜言柱.基于滑模变结构的永磁同步电机精确线性化控制[J].航空学报, 2008, 29(5): 1269-1274.
[145] Pisano A, Davila A, Fridman L, Usai E. Cascade Control of PM DC Drives Via Second-Order Sliding-Mode Technique [J]. IEEE Transactions on Industrial Electronics, 2008, 55(11): 3846-3854.
[146]王丰尧.滑模变结构控制[M].北京:机械工业出版社, 1995.
[147] Filippov A F. Differential Equations with Discontinuous Righthand Side [J]. American Mathematical Society Translations, 1964, 42(2): 199-231.
[148] Filippov A F. Differential Equations with Discontinuous Right-hand Sides [M]. Dordrecht, the Netherlands: Kluwer Academic, 1988.
[149] Levant A. Principles of 2-Sliding Mode Design [J]. Automatica, 2007, 43(4): 576-586.
[150] Reichhartinger M, Horn M. Application of Higher Order Sliding-Mode Concepts to a Throttle Actuator for Gasoline Engines [J]. IEEE Transaction on IndustrialElectronics, 2009, 56(9): 3322-3328.
[151] Emelyanov S V, Korovin S K, Levantovsky L V. Higher Order Sliding Regimes in The Binary Control Systems. Soviet Physics, Doklady, 1986, 31: 291-293.
[152] Man Z, Paplinski A P, Wu H. A Robust MIMO Terminal Sliding Mode Control for Rigid Robotic Manipulators [J]. IEEE Transactions on Automatic Control, 1994, 39(12), 2464-2468.
[153] Pisano A, Usai E. Sliding Mode Control: a Survey with Applications in Math [J]. Mathematics and Computers in Simulation, 2010, doi: 10.1016/j. matcom.2010.10.003.
[154]米阳,李文林,井元伟.基于幂次趋近律的一类离散时间系统的变结构控制[J].控制与决策, 2008, 23(6): 643-646.
[155] Bandyopadbyay B, Deepak F, Park Y J. A Robust Algorithm Against Actuator Saturation using Integral Sliding Mode and Composite Nonlinear Feedback [C]//Proceedings of the 17th World Congress The International Federation of Automatic Control. Seoul, Korea, 2008: 14174-14179.
[156] Bessa W M. Some Remarks on The Boundedness and Convergence Properties of Smooth Sliding Mode Controllers [J]. International Journal of Automation and Computing, 2009, 6(2): 154-158.
[157] Labiod S. Comments on“Integral Variable Structure Control of Nonlinear System using CMAC Neural Network Learning Approach”[J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, 2004, 34(6): 2421-2421.
[158] Liang C Y, Su J P. A New Approach to The Design of a Fuzzy Sliding Mode Controller [J]. Fuzzy Sets and Systems, 2003, 139(1): 111-124.
[159] Chen H M, Renn J C, Su J P. Sliding Mode Control with Varying Boundary Layers for an Electro-Hydraulic Position Servo System [J]. International Journal of Advanced Manufacturing Technology, 2005, 26(1): 117-123.
[160] Kachroo P, Tomizuka M. Chattering Reduction and Error Convergence in The Sliding-Mode Control of a Class of Nonlinear Systems [J]. IEEE Transactions on Automatic Control, 1996, 41(7): 1063-1068.
[161]冯勇,鲍晟,余星火.非奇异终端滑模控制系统的设计方法[J].控制与决策. 2002, 17(2): 192-198.
[162] Feng Y, Yu X, Man Z. Non-Singular Terminal Sliding Mode Control of Rigid Manipulators [J]. Automatica, 2002, 38(12): 2159-2167.
[163] Bailk C, Kim K H, Youn M J. Robust Nonlinear Speed Control of PM Synchronous Motor using Boundary Layer Integral Sliding Mode Control Technique [J]. IEEE Transactions on Control System Technology. 2000, 8(1): 47-54.
[164] Cho D, Kato Y, Spliman D. Sliding Mode and Classical Controller in MagneticLevitation Systems [J]. IEEE Control System Magazine. 1993, 13(1): 42-48.
[165] Lee J H. Highly Robust Position Control of BLDDSM using an Improved Integral Variable Structure System [J]. Automatica, 2006, 42(6): 929-935.
[166] Lu Y S. Integral Variable-Structure Control with Variable-Structure Sliding Dynamics for Antireset Windup [J]. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering. 2008, 222(3): 209-216.
[167] Makoto Y, Yuzuru T, Kiyohige S. A Design Method of Sliding Mode Controller for Servo-Systems Subject to Actuator Saturation [J]. JSME International Journal. Series C, Mechanical Systems, Machine Elements and Manufacturing, 2003, 46(3): 960– 966.
[168] Sun D, Hu S, Shao X, Liu C. Global Stability of a Saturated Nonlinear PID Controller for Robot Manipulators [J]. IEEE Transactions on Control System Technology, 2009, 17(4): 892-899.
[169]冯勇,安澄全,李涛.采用双滑模平面减小一类非线性系统稳态误差[J].控制与决策, 2000, 15(3): 361-364.
[170]高为炳.变结构控制的理论及设计方法[M].北京:科学出版社. 1998.
[171] Okabayshi R, Furuta K. Design of Sliding Mode Control Systems with Constrained Inputs [C]// Proceedings of the 35th IEEE Conference on Decision and Control. Kobe, Japan, 1996: 3492-3497.
[172] Kothare M V, Campo P J, Morari M. A Unified Framework for Study of the Anti-Windup Design [J]. Automatica, 1994, 30(12): 1869-1883.
[173] Peng Y, Viranir D, Hanus R. Anti-windup, Bumpless, and Conditional Transfer Techniques for PID Controller [J]. IEEE Control System Magazine, 1996, 16(4): 48-57.
[174] Lu Y S, Chen J S. Design of a Global Sliding-Mode Controller for a Motor Drive with Bounded Control [J]. International Journal of Control, 1995, 62(5): 1001-1019.
[175] Davila J, Fridman L, Levant A. Second-Order Sliding-Mode Observer for Mechanical Systems [J]. IEEE Transactions on Automatic Control, 2005, 50(11): 1785-1789.
[176] Davila J, Fridman L, Poznyak A. Observation and Identification of Mechanical Systems via Second Order Sliding Modes [J]. International Journal of Control, 2006, 79(10): 1251-1262.
[177] Wu Q, Saif M. Robust Fault Diagnosis of a Satellite System Using a Learning Strategy and Second Order Sliding Mode Observer [J]. IEEE Systems Journal, 2010, 4(1): 112-121.
[178] Levant A. Homogeneity Approach to High-Order Sliding Mode Design [J].Automatica, 2005, 41(5): 823-830.
[179] Kobayashi S, Furuta K. Frequency Characteristics of Levant’s Differentiator and Adaptive Sliding Mode Differentiator [J]. International Journal of Systems Science, 2007, 38(10): 825-832.
[180] Shtessel Y B, Moreno J A, Plestan F, Fridman L M, Poznyak A S. Supper-twisting Adaptive Sliding Mode Control: A Lyapunov Design [C]//Proceedings of the 48th IEEE Conference on Decision and Control, Atlanta, USA, 2010: 5109-5112.
[181]俞立.鲁棒控制—线性矩阵不等式处理方法[M].北京:清华大学出版社, 2002.
[182]刘智平,周凤歧,周军.具有参数不确定性的飞行器的变结构姿态控制[J].宇航学报, 2007, 28(1): 43-48.
[183]张友安,王宏然,程继红.应用动态逆和三时标分离的飞航导弹过载控制离散化设计[J].吉林大学学报(工学版), 2006, 36(6): 1008-1013.
[184] Singh S N, Steinberg M L, Page A B. Nonlinear Adaptive and Sliding Mode Flight Path Control of F/A-18 Model [J]. IEEE Transactions on Aerospace and Electronic Systems, 2003, 39(4): 1250-1262.
[185] Levant A. Non-Homogeneous Finite-Time-Convergent Differentiator. Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference. Shanghai, P.R. China, December 16-18, 2009: 8399-8404.
[186] Dorsett K M, Mehl D R. Innovative Control Effectors (ICE), Final Report for September 1994-January 1996, Wright Laboratory, Air Force Material Command, WL-TR-96-3043, January 1996.
[187] Jovan D. BoSkovic, Sai-Ming Li, and Raman K. Mehra. Study of an Adaptive Reconfigurable Control Scheme for Tailless Advanced Fighter Aircraft (TAFA) in the Presence of Wing Damage.
[188]杨晖.先进重构飞行控制技术和方法研究[J].飞行力学, 2001, 19(4): 11-14.
[189] http://www.defence.org.cn/article-1-61696.html
[190]Willard J. Harris. X-36 Tailless Agility Aircraft Subsystems Integration[C]// Proceedings of the AIAA Guidance, Navigation, and Control Conference, AIAA 97-5505, 1997.
[191] http://www.airforce-technology.com/projects/x-45-ucav/
[192] Chen W H. Nonlinear Disturbance Observer Enhanced Dynamic Inversion Control [J]. AIAA Journal of Guidance, Control, and Dynamic Systems, 2003, 26(1): 161-166.
[193]陈谋,姜长生,吴庆宪.基于干扰观测器的一类不确定非线性系统鲁棒H∞控制[J].控制理论与应用,2006,23(4): 611-615.
[194] Reiner J, Balas G J, Garrard, W L. Flight Control Design Using Robust DynamicInversion and Time-scale Separation [J]. Automatica, 1996, 32(11): 1493–1504.
[195] Boskovic J D, Li S M, Raman K M. Robust Tracking Control Design for Spacecraft under Control Input Saturation [J]. AIAA Journal of Guidance, Control, and Dynamics, 2004, 27 (4): 627-633.
[196] Hess R A, Vetter T K, Wells S R. Design and Evaluation of a Damage Tolerant Flight Control System[C]//Proceedings of AIAA Guidance, Navigation, and Control Conference and Exhibit, Providence, Rhode Island, 2004: 1-21.
[197] Shen Y J, Xia X H. Semi-Global Finite-Time Observer for Nonlinear Systems [J]. Automatica, 2008, 44(12): 3152-3156.
[198] Bhat S, Bernstein D S. Finite-Time Stability of Continuous Autonomous Systems [J]. SIAM Journal on Control and Optimization, 2000, 38(3): 751-766.
[199] Bhat S, Bernstein D S. Finite Time Stability of Homogeneous Systems [C]//Proceedings of American Control Conference, Albuquerque, New Mexico, 1997: 602-609.
[200] Bhat S, Bernstein D S. Geometric Homogeneity with Applications to Finite-Time Stability [J]. Math. Control Signals Systems, 2005, 17(2): 101-127.
[201]李世华,丁世宏,田玉平.一类二阶非线性系统的有限时间状态反馈镇定方法[J].自动化学报, 2007, 33(1): 101-104.
[202] Zhang H, Wang X, Han D. Dual-Quaternion-Based Variable Structure Control: A New Approach and Application [C]//Proceedings of 2010 International Conference on Intelligent Robotics and Applications, Shanghai, China, 2010: 75-86.
[203] Athans M, Falb P L. Optimal Control: An Introduction to the Theory and Its Applications [M], New York: McGraw-Hill. 1966.
[204] Bhat S P, Berstein D S. Continuous Finite-Time Stabilization of the Translation and Rotational Double Integrator [J]. IEEE Transaction on Automatic Control, 1998, 43(5): 678-682.
[205] Rekasius Z V. An Alternate Approach to the Fixed Terminal Point Regulator Problem [J]. IEEE Transaction on Automatic Control, 1964, 9(3): 290-292.
[206] Bhat S P, Berstein D S. Geometric Homogeneity with Applications to Finite Time Stability [J]. Math. Control Signals Systems, 2005, 17(2): 101-127.
[207] Huang X, Lin W, Yang B, Global Finite-Time Stabilization of a Class of Uncertain Nonlinear Systems [J]. Automatica, 2005, 41(5): 881-888.
[208]王新华,陈增强,袁著祉.全程快速非线性跟踪-微分器[J].控制理论与应用,2003, 12(6): 875-878.
[209] Qian C, Lin W. A Continuous Feedback Approach to Global Strong Stabilization of Nonlinear Systems [J]. IEEE Transactions on Automatic Control, 2001, 46(7): 1061-1079.
[210] Bhat S P, Bernstein D S. Finite-Time Stability of Continuous AutonomousSystems [J]. SIAM Journal on Control Optimization, 2000, 38(3): 751-766.
[211] Qian C, Lin W. Non-Lipschitz Continuous Stabilizers for Nonlinear Systems with Uncontrollable Unstable Linearization [J]. Systems & Control Letters, 2001, 42(3): 185-200.
[2] Camacho E F, Bordons C. Model Predictive Control [M]. Berlin: Speinger-Verlag, 2004.
[3] Krstic M, Kanellakopoulos I, Kokotovic P. Nonlinear and Adaptive Control Design [M]. New York: Wiley, 1995.
[4] Utkin V. Sliding Mode in Control and Optimization [M]. Berlin: Springer-Verlag, 1992.
[5] Draznenovic B.The Invariance Conditions in Variable Structure Control Systems [J].Automatica, 1969, 5(2): 287-295.
[6] Isidori A. Nonlinear Control Systems [M]. Berlin: Springer-Verlag, 1995.
[7]张文修,梁广锡.模糊控制与系统[M].西安:西安交通大学出版社, 1998.
[8] Emel'yanov S V, Taran V A. On a Class of Variable Structure Control Systems. In: USSR Academy of Sciences, Energy and Automation. Moskov, 1962. (in Russian)
[9] Emel'yanov S V. Theory of Variable Structure Systems [M]. Moscow: Nauke, 1970.
[10] Utkin V I. Sliding Modes and Their Application in Variable Structure Systems [M]. Moscow: Nauka, 1970. (in Russian).
[11] Itkis U. Control Systems of Variable Structure [M]. New York: Wiley, 1976.
[12] Utkin V I. Variable Structure Systems with Sliding Modes [J]. IEEE Transactions on Automatic Control, 1977, 22(2), 212-222.
[13] Pan S, Su H, Hu X, Chu J. Variable Structure Control Theory and Application: A Suvery [C]//Proceedings of the 3rd World Congress on Intelligent Control and Automation, Heifei, P.R.China, 2000: 2977-2981.
[14]高为炳.变结构控制理论基础[M].北京:中国科学技术出版社, 1990.
[15]胡跃明,周其节.分布参数变结构控制系统[M].北京:国防工业出版社, 1996.
[16]姚琼荟,黄继起,吴汉松.变结构控制系统[M].重庆:重庆大学出版社, 1997.
[17]胡跃明.变结构控制理论与应用[M].北京:科学出版社, 2003.
[18]刘金琨.滑模变结构控制Matlab仿真[M].北京:清华大学出版社, 2005.
[19]傅春,谢剑英.模糊滑模控制研究综述[J].信息与控制, 2001, 30(5): 434-440.
[20]张晓宇,苏宏业.滑模变结构控制理论进展综述[J].化工自动化及仪表. 2006, 33(2): 1-8.
[21]刘金琨,孙富春.滑模变结构控制理论及其算法研究与进展[J].控制理论与应用, 2007, 24(3): 407-419.
[22] Yu X, Kaynak O. Sliding-Mode Control with Soft Computing: A Survey [J]. IEEETransactions on Industrial Electronics, 2009, 56(9): 3275-3285.
[23] Young K D, Utkin V I, Ozguner U. A Control Engineer’s Guide to Sliding Mode Control [J]. IEEE Transaction on Control Systems Technology, 1999, 7(3): 328-342.
[24] Slotine J J E, Sastry S S. Tracking Control of Nonlinear Systems using Sliding Surfaces with Application to Robot Manipulator [J]. International Journal of Control, 1983, 38(2): 465-492.
[25] Slotine J J E. Sliding Controller Design for Non-linear Systems [J]. International Journal of Control, 1984, 40(2): 421-434.
[26] Chen M S, Hwang Y R, Tomizuka M. A State-Dependent Boundary Layer Design for Sliding Mode Control [J]. IEEE Transaction on Automatic Control, 2002, 47(10): 1677-1681.
[27] Chen M S, Hwang Y R, Tomizuka M. Sliding Mode Control Reduced Chattering For Systems With Dependent Uncertainties [C]//Proceedings of the 2004 IEEE International Conference on Networking, Sensing & Control, Taipei, Taiwan, 2004: 967-971.
[28] Lee H, Kim E, Kang H J, Park M. A New Sliding-Mode Control with Fuzzy Boundary Layer [J], Fuzzy Sets and Systems, 2001, 120(1): 135-143.
[29] Cupertino F, Naso D, Mininno E, Turchiano B. Sliding-Mode Control with Double Boundary Layer for Robust Compensation of Payload Mass and Friction in Linear Motors [J]. IEEE Transactions on Industry Applications, 2009, 45(5): 1688-1696.
[30] Benayache R, Chrifi-Alaoui L, Bussy P, Castelain J M. Design and Implementation of Sliding Mode Controller with Varying Boundary Layer for a Coupled Tanks Systems[C]//17th Mediterranean Conference on Control & Application, Thessaloniki, Greece, 2009: 1215-1220.
[31] Gao W, Hung J C, Variable Structure Control of Nonlinear Systems: A New Approach [J]. IEEE Transactions on Industrial Electronics, 1993, 40(1): 45-55.
[32]李文林,李巧萍.可抑制抖振的滑动模态到达条件[C]//Proceedings of the 27th Chinese Control Conference, Kunming, China, 2008: 154-158.
[33] Yu S, Yu X, Shirinzadeh B, Man Z. Continuous Finite-Time Control for Robotic Manipulators with Terminal Sliding Mode [J]. Automatica, 2005, 41(11): 1957-1964.
[34]梅红,王勇.快速收敛的机器人滑模变结构控制[J].信息与控制, 2009, 38(5): 522-558.
[35] Tsai C H, Chung H Y, Yu F M. Neural-Sliding Mode Control with Its Applications in Seesaw Systems [J]. IEEE Transactions on Neural Networks, 2004, 15(1): 124-134.
[36] Fang Y, Chow T W S, Li X D. Use of a Recurrent Neural Network in DiscreteSliding-Mode Control [J]. IEE Control Theory and Applications, 1999, 146(1): 84-90.
[37]刘殿通,易建强,谭民.一类非线性系统的自适应滑模模糊控制[J].自动化学报, 2004, 30(1): 143-150.
[38] Hwang Y R, Tomizuka M. Fuzzy Smoothing Algorithms for Variable Structure Systems [J]. IEEE Transactions on Fuzzy Systems, 1994, 2(4): 277-284.
[39] Wu J, Ham T S. A Sliding-Mode Approach to Fuzzy Control Design [J], IEEE Transaction on Control Systems Technology, 1996, 4(2): 141-151.
[40] Wai R J. Adaptive Fuzzy Sliding-Mode Control for Electrical Servo Drive [J]. IEEE Transaction on Industry Electronic, 2007, 54(1): 586-594.
[41] Sadati N, Ghadami R. Adaptive Multi-Model Sliding Mode Control of Robotic Manipulators using Soft Computing [J]. Neurocomputing, 2008, 71(2): 2702-2710.
[42]张金萍,刘阔,林剑锋,马晓波,于文东.挖掘机的4自由度自适应模糊滑模控制[J].机械工程学报, 2010, 46(21): 87-92.
[43] Lin S C, Chen Y Y. Design of Self-Learning Fuzzy Sliding Mode Controllers Based on Genetic Algorithm [J]. Fuzzy Sets Systems, 1997, 86(2): 139-153.
[44] Xu J X, Lee T H, Wang M, Yu X H. Design of Variable Structure Controllers with Continuous Switching Control [J]. International Journal of Control, 1996, 65(3): 409-431.
[45] Furuta K, Pan Y. Sliding Sectors for VS Controller [J]. Automatica, 2000, 36(2): 211-228.
[46] Pan Y, Kumar D, Liu G, Furuta K. Design of Variable Structure Control System with Nonlinear Time-Varying Sliding Sector [J]. IEEE Transactions on Automatic Control, 2009, 54(8): 1981-1986.
[47] Kang B P, Ju J L. Sliding Mode Controller with Filtered Signal for Robot Manipulators using Virtual Plant/Controller [J]. Mechatronics, 1997, 7(3): 277-286.
[48] Yanada H, Ohnishi H. Frequency-Shaped Sliding Mode Control of an Electrohydraulic Servomotor [J]. Journal of Systems and Control and Dynamics, 1991, 213(1): 441-448.
[49] Korondi P, Young D, Hashimoto H. Sliding Mode Based Disturbance Observer for Motion Control [C]//Proceedings of the 37th IEEE Conference on Decision and Control, Florida, USA, 1998: 1926-1927.
[50] Eun Y, Kim J H, Kim K, Cho D H. Discrete-Time Variable Structure Controller with a Decoupled Disturbance Compensator and Its Applications to a CNC Servomechanism [J]. IEEE Transactions on Control Systems Technology, 1999, 7(4): 414-422.
[51]宋立忠,陈少昌,姚琼荟.多输入不确定系统离散变结构控制设计[J].控制与决策, 2003, 18(4): 468-471.
[52] Koshkouei A J, Burnham K J, Zinober A S I. Dynamic Sliding Mode Control Design [J]. IEE Proceedings - Control Theory and Applications, 2005, 152(4): 392-396.
[53] Bregeault V, Plestan F, Shtessel Y B, Poznyak A. Adaptive Sliding Mode Control for an Electropneumatic Actuator [C] // Proceedings of 2010 11th International Workshop on Variable Structure Systems, Mexico City, Mexico, 2010: 260-265.
[54] Yoo D S, Chung M J. A Variable Structure Control with Simple Adaptation Laws for Upper Bounds on the Norm of the Uncertainties [J]. IEEE Transaction on Automatic Control, 1992, 37(6): 860-865.
[55] Su C Y, Leung T P. A Sliding Mode Controller with Bound Estimation for Robot Manipulators [J]. IEEE Transaction on Robotics and Automation, 1993, 9(2): 208-214.
[56] Wheeler G, Su C Y, Stepanenko Y. A Sliding Mode Controller with Improved Adaptation Laws for the Upper Bounds on the Norm of Uncertainties [J]. Automatica, 34(2): 1657-1661.
[57] Munoz D, Sbarbaro D. An Adaptive Sliding Mode Controller for Discrete Nonlinear Systems [J]. IEEE Transactions on Industrial Electronics, 2000, 47(3): 574-581.
[58] Tao C W, Chan M L, Lee T T. Adaptive Fuzzy Sliding Mode Controller for Linear Systems with Mismatched Time-Varying Uncertainties [J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, 2003, 33(2): 283-294.
[59] Lin F J, Chiu S L. Novel Sliding Mode Controller for Synchronous Motor Drive [J]. IEEE Transactions on Aerospace and Electronic Systems, 1998, 34(2): 532-542.
[60] Lin F J, Chou W D, Huang P K. Adaptive Sliding-Mode Controller Based on Real-Time Genetic Algorithm for Induction Motor Servo Drive [J]. IEE Proceedings B Electric Power Applications, 2003, 150(1): 1-13.
[61] Huang Y J, Kuo T C, Chang S H. Adaptive Sliding-Mode Control for Nonlinear Systems with Uncertain Parameters [J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, 2008, 38(2): 534-539.
[62] Plestan F, Shtessel Y B, Bregeault V, Poznyak A. New Methodologies for Adaptive Sliding Mode Control [J]. International Journal of Control, 2010, 83(9): 1907-1919.
[63] Lee H, Utkin V I. Chattering Suppression Methods in Sliding Mode Control Systems [J]. Annual Reviews in Control, 2007, 31(2): 179-188.
[64] Ambrosino G, Celektano G, Garofalo F. Variable Structure Model Reference Adaptive Control Systems [J]. International Journal of Control, 1984, 39(6): 1139-1349.
[65] Liu H. Variable Structure Model-Reference Adaptive Control (VS-MRAC) Using Only Input and Output Measurements: The General Case [J]. IEEE Transactions on Automatic Control, 1990, 35(11): 1238-1243.
[66] Liu H. Lizarralde F, DeAraujo A D. New Results on Output-Feedback Variable Structure Model-Reference Adaptive Control: Design and Stability Analysis [J]. IEEE Transactions on Automatic Control, 1997, 42(3): 1-7.
[67]林岩,毛剑琴,操云甫.鲁棒低增益变结构模型参考自适应控制[J].自动化学报, 2001, 27(5): 665-671.
[68]张达科,胡跃明,吴捷,郭华芳.类反斜线回滞系统的模型参考滑模控制[J].控制理论与应用, 2005, 22(3): 402-407.
[69] Khalil H K. Nonlinear Systems [M], 3rd Ed, Upper Saddle River, New Jersey:Prentice-Hall, 2002.
[70] Chern T L, Wu Y C. Design of Integral Variable Structrue Controller and Application to Electrohydraulic Velocity Servosystems [J]. IEE Proceedings D Control Theory and Applications, 1991, 138(5): 439-444.
[71] Chern T L, Wu Y C. Integral Variable Structure Control Approach for Robot Manipulators [J], IEE Proceedings D Control Theory and Applications, 1992, 139(2): 161-166.
[72] Chern T L, Wu Y C. Design of Brushless DC Position Servo Systems using Integral Variable Structure Approach [J]. IEE Proceedings B Electric Power Applications, 1993, 140(1): 27-34.
[73] Chern T L, Chang J, Chang G K. DSP-Based Integral Variable Structure Model Following Control for Brushless DC Motor Drivers [J]. IEEE Transactions on Power Electronics, 1997, 12(1): 53-63.
[74] Wang J D, Lee T L, Juang Y T. New Methods to Design an Integral Variable Structure Controller [J]. IEEE Transactions on Automatic Control, 1996, 41(1): 140-143.
[75] Lee J H, Allaire P E, Tao G, Zhang X. Integral Sliding-Mode Control of a Magnetically Suspended Balance Beam: Analysis, Simulation, and Experiment. IEEE/ASME Transactions on Mechatronics, 2001, 6(3): 338-346.
[76] Slotine J J. Li W P. Applied Nonlinear Control [M]. New Jersey: Prentice-Hall, 1991.
[77] Bouri M, Thomasset D. Sliding Control of an Electropneumatic Actuator Using an Integral Switching Surface [J]. IEEE Transactions on Control Systems Technology, 2001, 9(2): 368-375.
[78]张天平,梅建东,沈启坤.具有模糊监督控制器的积分变结构间接自适应控制[J].控制理论与应用, 2007, 24(1): 90-95.
[79]管成,潘双夏.含有非线性不确定参数的电液系统滑模自适应控制[J].控制理论与应用, 2008, 25(2): 261-267.
[80] Hung C P. Integral Variable Structure Control of Nonlinear System Using a CMAC Neural Network Learning Approach [J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, 2004, 34(1): 702-709.
[81] Stepanenko Y, Cao Y, Su C. Variable Structure Control of Robotic Manipulator with PID Sliding Surfaces [J]. International Journal of Robust and Nonlinear Control, 1998, 8(1): 79-90.
[82] Parra-Vega V, Arimoto S, Liu Y H, Hirzinger G, Akella P. Dynamic Sliding PID Control for Tracking of Robot Manipulators: Theory and Experiments [J]. IEEE Transactions on Robotics and Automation, 2003, 19(6): 967-976.
[83] Eker I. Sliding Mode Control with PID Sliding Surface and Experimental Application to an Electromechanical Plant [J]. ISA Transactions, 2006, 45(1): 109-118.
[84]王敏,杜克林,黄心汉.机器人滑模轨迹跟踪控制[J].机器人, 2001, 23(3): 217-222.
[85] Utkin V, Shi J. Integral Sliding Mode in Systems Operating under Uncertainty Conditions [C]//Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan, 1996: 4591-4596.
[86] Yahaya M S, Johari O, Ruddin A G. A Class of Proportional-Integral Sliding Mode Control with Application to Active Suspension System [J]. Systems & Control Letters, 2004, 51(3/4): 217-223.
[87] Niu Y, Daniel W C, Lam J. Robust Integral Sliding Mode Control for Uncertain Stochastic Systems with Time-Varying Delay [J]. Automatica, 2005, 41(5): 873-880.
[88] Comanescu M, Xu L, Batzel T D. Decoupled Current Control of Sensorless Induction-Motor Drives by Integral Sliding Mode [J]. IEEE Transactions on Industrial Electronics, 2008, 55(11): 3836-3845.
[89] Seshagiri S, Khalil H K. On introducing Integral Action in Sliding Mode Control [C]//Proceedings of the 41st IEEE Conference on Decision and Control, Nevada, USA, 2002: 1473-1478.
[90] Levant A. Sliding Order and Sliding Accuracy in Sliding Mode Control [J]. International Journal of Control, 1993, 58(6): 1247-1263.
[91] Levantovsky L V (Levant A). Higher Order Sliding Modes and Their Application for Controlling Uncertain Processes [D]. Ph.D. Dissertation, Institute for system studies of the USSR Academy of Science, Moscow, 1987.
[92] Fridman L, Levant A. Higher order Sliding Modes as the Natural Phenomena of Control Theory [C] //Proceedings of the Workshop Variable Structure and Lyapunov Technique, Benevento, 1994: 302-309.
[93] Bartolini G, Pisano A, Punta E, Usai E. A Survey of Application of Second-Order Sliding Mode Control to Mechanical Systems [J]. International Journal of Control, 2003, 76(9/10): 875-982.
[94] Levant A. Robust exact differentiation via Sliding Mode Technique [J]. Automatica, 1998, 34(3): 379-384.
[95] Levant A. Universal SISO Sliding-Mode Controllers with Finite-Tine Convergence [J]. IEEE Transactions on Automatic Control, 2001, 46(9): 1447-1451.
[96] Levant A. Higher Order Sliding Modes, Differentiation and Output-Feedback Control [J]. International Journal of Control, 2003, 76(9/10): 924-941.
[97] Man Z, Paplinski A P, Wu H. A Robust MIMO Terminal Sliding Mode Control for Rigid Robotic Manipulators [J]. IEEE Transactions on Automatic Control, 1994, 39(12): 2464-2468.
[98] Bartolini G, Ferrara, A, Usai, E. Output Tracking Control of Uncertain Nonlinear Second-Order Systems [J]. Automatica, 1997, 33(12): 2203–2212.
[99] Bartolini G, Ferrara A, Usai, E. Chattering Avoidance by Second-Order Sliding Mode Control [J]. IEEE Transactions on Automatic Control, 1998, 43(2): 241-246.
[100] Shtessel Y B, Shkolnikov I A, Brown M J. An Asymptotic Second-Order Smooth Sliding Mode Control [J]. Asian Journal of Control, 2003, 5(4): 498-504.
[101] Shtessel Y B, Shkolnikov I A, Levant A. Smooth Second Modes: Missile Guidance Application [J]. Automatica, 2007, 43(8): 1470-1476.
[102] Shtessel Y B, Tournes C H. Integrated Higher-Order Sliding Mode Guidance and Autopilot for Dual-Control Missiles [J]. AIAA Journal of Guidance, Control, and Dynamics, 2009, 32(1): 79-94.
[103] Shtessel Y B, Shkolnikov I A, Levant A. Guidance and Control of Missile Interceptor using Second-Order Sliding Modes [J]. IEEE Transactions on Aerospace Electronic Systems, 2009, 45(1): 110-123.
[104] Pan Y, Liu G, Kumar K D. Robust Stability Analysis of Asymptotic Second-order Sliding Mode Control System Using Lyapunov Function [C]// Proceeding of the 2010 IEEE International Conference on Information and Automation, Harbin, China, 2010: 313-318.
[105] Plestan F, Moulay E, Glumineau A, Cheviron T. Robust Output Feedback Sampling Control Based on Second-Order Sliding mode [J]. Automatica, 2010, 46(6): 1096-1100.
[106] Plestan F, Glumineau A. A New Differentiator Based on a Second Order Sliding Mode Output Feedback Control [C]//Proceedings of 49th IEEE Conference on Decision and Control, Atlanta, USA, 2010.
[107] Polyakov A, Poznyak A. Lyapunov Function Design for Finite-Time Convergence Analysis:“Twisting”Controller for Second-Order Sliding Mode Realization [J]. Automatica, 2009, 45(2): 444-448.
[108] Polyakov A, Poznyak A. Reaching Time Estimation for“Super-Twisting”Second Order Sliding Mode Controller via Lyapunov Function Designing [J], IEEE Transactions on Automatic Control, 2009, 54(8): 1951-1955.
[109] Jaime A M, Marisol O. A Lyapunov Approach to Second Order Sliding Mode Controllers and Observers [C]//Proceedings of the IEEE International Conference on Decision and Control. New York, USA, 2008: 2856-2861.
[110] Davila A, Jaime A M, Fridman L. Optimal Lyapunov Function Selection for Reaching Time Estimation of Supper Twisting Algorithm[C]//Proceedings of Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference. Shanghai, China, 2009: 8045-8410.
[111] Bartolini G, Pisano A, Usai E. On the Finite-Time Stabilization of Uncertain Nonlinear Systems with Relative Degree Three [J]. IEEE Transactions on Automatic Control, 2007, 52(11): 2134-2141.
[112] Bartolini G, Pillosu S, Pisano A, Usai E. Time-Optimal Stabilization for a Third-Order Integrator: a Robust State-Feedback Implementation [M], in Dynamics, Bifurcations and Control, Lecture Notes in Control and Information Sciences, Springer-Verlag, 2002, 273: 131-144.
[113] Levant A. Quasi-Continuous Higher-Order Sliding-Mode Controllers [J], IEEE Transactions on Automatic Control, 2005, 50(11): 1812-1816.
[114] Levant A, Alelishvili L. Integral High-Order Sliding Modes [J], IEEE Transaction on Automatic Control, 2007, 52(7): 1278-1282.
[115] Laghrouche S, Plestan F, Glumineau A. Practical Higher Order Sliding Mode Control: Optimal Control Based Approach and Application to Electromechanical Systems. In: Edwards, Fossas Colet, & Fridman (Eds.), Advances in Variable Structure and Sliding Mode Control. Lecture Notes in Control and Information Sciences: (vol. 334), Berlin: Springer. 2006.
[116] Laghrouche S, Plestan F, Glumineau A. Higher Order Sliding Mode Control Based on Integral Sliding Mode [J]. Automatica, 2007, 43(3): 531-537.
[117] Plestan F, Glumineau A, Laghrouche S. A New Algorithm for High-Order Sliding Mode Control [J]. International Journal of Robust and Nonlinear Control, 2008, 18(4/5): 441-453.
[118] Defoort M, Floquet T, Kokosy A, Perruquetti W. A Novel Higher Order Sliding Mode Control Scheme [J]. Systems & Control Letter, 2009, 58(2): 102-108.
[119]丁世宏,李世华.有限时间控制问题综述[J].控制与决策, 2011, 26(2): 161-169.
[120] Dinuzzo F, Ferrara A. Higher Order Sliding Mode Controllers with Optimal Reaching [J]. IEEE Transactions on Automatic Control, 2009, 54(9): 2126-2136.
[121] Zong Q, Zhao Z -S, Zhang J. Higher Order Sliding Mode Control with Self-tuningLaw Based on Integral Sliding Mode [J]. IET Control Theory and Applications, 2010, 4(7): 1282-1289.
[122]陈杰,李志平,张国柱.不确定非线性系统的高阶滑模控制器设计[J].控制理论与应用,2010, 27(5): 563-570.
[123] Brierley S D, Longchamp R. Application of Sliding-Mode Control to Air-Air Interception Problem [J]. IEEE Transaction on Aerospace and Electronic Systems, 1990, 26(2): 306-325.
[124] Zhou D, Mu C D, Xu W L. Adaptive Sliding-Mode Guidance of a Homing Missile [J]. AIAA Journal of Guidance, Control, and Dynamics, 1999, 22(4): 589-594.
[125]孙未蒙,郑志强.一种多约束条件下的三维变结构制导律[J].宇航学报, 2007, 28(2): 344-349.
[126]周军,王婷.基于二阶滑模控制的驾束制导导弹一体化制导系统设计[J].宇航学报,2007, 28(6): 1632-1637.
[127] Shtessel Y B, Shkolnikov I A. Aeronautical and Space Vehicle Control in Dynamic Sliding Manifolds [J]. International Journal of Control, 2003, 76(9/10): 1000-1017.
[128] Pukdeboon C, Zinober A S I, Thein M–W. Quasi-Continuous Higher Order Sliding-Mode Controllers for Spacecraft-Attitude-Tracking Maneuvers [J], IEEE Transaction on Industrial Electronics, 2010, 57(4): 1436-1444.
[129] Hall C, Shtessel Y B. Sliding Mode Disturbance Observers-based Control for a Reusable Launch Vehicle [J]. AIAA Journal on Guidance, Control, and Dynamics, 2006, 29(6): 1315-1329.
[130] Shtessel Y B, Buffington J, Banda S. Tailless Aircraft Flight Control Using Multiple Time Scale Re-configurable Sliding Modes [J]. IEEE Transactions on Control Systems Technology, 2002, 10(2): 288-296.
[131] Massey T, Shtessel Y B. Continuous Traditional and High Order Sliding Modes for Satellite Formation Control [J]. AIAA Journal on Guidance, Control, and Dynamics, 2005, 28(4): 826-831.
[132] Haerlian F, Achour K, Floquet T, Perruquetti W. Higher Order Sliding Mode Control of Wheeled Mobile Robots in the Presence of Sliding Effects [C]// Proceeding of the 44th IEEE Conference on Decision and Control, and European Control Conference, Seville, Spain, 2005: 1959-1963.
[133] Lee S U, Chang P H. Control of a Heavy-Duty Robotic Excavator using Time Delay Control with Integral Sliding Surface [J]. Control Engineering Practice, 2002, 10(7) : 679-711.
[134] Ferrara A, Magnani L. Motion Control of Rigid Robot Manipulators via First and Second Order Sliding Modes [J]. Journal of Intelligent Robot Systems, 2007, 48(1):23-36.
[135]胡跃明,晁红敏,李志权,梁天培.非线性仿射控制系统的高阶滑模控制[J].自动化学报, 2002, 28(3): 1-6.
[136] Butt Q R, Bhatti A I. Estimation of Gasoline-Engine Parameters Using Higher Order Sliding Mode [J]. IEEE Transactions on Industrial Electronics, 2008, 55(11): 3891-3898.
[137] Yagiz N, Hacioglu Y, Taskin Y. Fuzzy Sliding-Mode Control of Active Suspensions [J]. IEEE Transactions on Industrial Electronics, 2008, 55(11): 3883-3890.
[138] Pisano A, Usai E. Output-Feedback Control of an Underwater Vehilce Prototype by Higher-Order Sliding Modes [J]. Automatica, 2004, 40(9): 1525-1531.
[139] Bartolini G, Pisano A. Black-Box Position and Attitude Tracking for Underwater Vehicles by Second-Order Sliding-Mode Technique [J]. International Journal of Robust and Nonlinear Control. 2010, 20(14): 1594-1609.
[140] Ignaciuk P, Bartoszewicz A. Sliding-Mode Controller for Connection-Oriented Communication Networks [J]. IEEE Transactions on Industrial Electronics, 2008, 55(11): 4013-4021.
[141] Pan Y, Ozguner U, Dagci O H. Variable-Structure Control of Electronic Throttle Valve [J]. IEEE Transactions on Industrial Electronics, 2008, 55(11): 3899-3907.
[142]王江,曾启明.基于奇异摄动方法的同步电机二阶滑模控制器的设计[J].中国电机工程学报, 2003, 23(10): 142-148.
[143]孙宜标,杨雪,夏加宽.采用鲁棒微分器的永磁直线同步电机二阶滑模控制[J].中国电机工程学报, 2007, 27(33): 6-11.
[144]刘贤兴,胡育文,卜言柱.基于滑模变结构的永磁同步电机精确线性化控制[J].航空学报, 2008, 29(5): 1269-1274.
[145] Pisano A, Davila A, Fridman L, Usai E. Cascade Control of PM DC Drives Via Second-Order Sliding-Mode Technique [J]. IEEE Transactions on Industrial Electronics, 2008, 55(11): 3846-3854.
[146]王丰尧.滑模变结构控制[M].北京:机械工业出版社, 1995.
[147] Filippov A F. Differential Equations with Discontinuous Righthand Side [J]. American Mathematical Society Translations, 1964, 42(2): 199-231.
[148] Filippov A F. Differential Equations with Discontinuous Right-hand Sides [M]. Dordrecht, the Netherlands: Kluwer Academic, 1988.
[149] Levant A. Principles of 2-Sliding Mode Design [J]. Automatica, 2007, 43(4): 576-586.
[150] Reichhartinger M, Horn M. Application of Higher Order Sliding-Mode Concepts to a Throttle Actuator for Gasoline Engines [J]. IEEE Transaction on IndustrialElectronics, 2009, 56(9): 3322-3328.
[151] Emelyanov S V, Korovin S K, Levantovsky L V. Higher Order Sliding Regimes in The Binary Control Systems. Soviet Physics, Doklady, 1986, 31: 291-293.
[152] Man Z, Paplinski A P, Wu H. A Robust MIMO Terminal Sliding Mode Control for Rigid Robotic Manipulators [J]. IEEE Transactions on Automatic Control, 1994, 39(12), 2464-2468.
[153] Pisano A, Usai E. Sliding Mode Control: a Survey with Applications in Math [J]. Mathematics and Computers in Simulation, 2010, doi: 10.1016/j. matcom.2010.10.003.
[154]米阳,李文林,井元伟.基于幂次趋近律的一类离散时间系统的变结构控制[J].控制与决策, 2008, 23(6): 643-646.
[155] Bandyopadbyay B, Deepak F, Park Y J. A Robust Algorithm Against Actuator Saturation using Integral Sliding Mode and Composite Nonlinear Feedback [C]//Proceedings of the 17th World Congress The International Federation of Automatic Control. Seoul, Korea, 2008: 14174-14179.
[156] Bessa W M. Some Remarks on The Boundedness and Convergence Properties of Smooth Sliding Mode Controllers [J]. International Journal of Automation and Computing, 2009, 6(2): 154-158.
[157] Labiod S. Comments on“Integral Variable Structure Control of Nonlinear System using CMAC Neural Network Learning Approach”[J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, 2004, 34(6): 2421-2421.
[158] Liang C Y, Su J P. A New Approach to The Design of a Fuzzy Sliding Mode Controller [J]. Fuzzy Sets and Systems, 2003, 139(1): 111-124.
[159] Chen H M, Renn J C, Su J P. Sliding Mode Control with Varying Boundary Layers for an Electro-Hydraulic Position Servo System [J]. International Journal of Advanced Manufacturing Technology, 2005, 26(1): 117-123.
[160] Kachroo P, Tomizuka M. Chattering Reduction and Error Convergence in The Sliding-Mode Control of a Class of Nonlinear Systems [J]. IEEE Transactions on Automatic Control, 1996, 41(7): 1063-1068.
[161]冯勇,鲍晟,余星火.非奇异终端滑模控制系统的设计方法[J].控制与决策. 2002, 17(2): 192-198.
[162] Feng Y, Yu X, Man Z. Non-Singular Terminal Sliding Mode Control of Rigid Manipulators [J]. Automatica, 2002, 38(12): 2159-2167.
[163] Bailk C, Kim K H, Youn M J. Robust Nonlinear Speed Control of PM Synchronous Motor using Boundary Layer Integral Sliding Mode Control Technique [J]. IEEE Transactions on Control System Technology. 2000, 8(1): 47-54.
[164] Cho D, Kato Y, Spliman D. Sliding Mode and Classical Controller in MagneticLevitation Systems [J]. IEEE Control System Magazine. 1993, 13(1): 42-48.
[165] Lee J H. Highly Robust Position Control of BLDDSM using an Improved Integral Variable Structure System [J]. Automatica, 2006, 42(6): 929-935.
[166] Lu Y S. Integral Variable-Structure Control with Variable-Structure Sliding Dynamics for Antireset Windup [J]. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering. 2008, 222(3): 209-216.
[167] Makoto Y, Yuzuru T, Kiyohige S. A Design Method of Sliding Mode Controller for Servo-Systems Subject to Actuator Saturation [J]. JSME International Journal. Series C, Mechanical Systems, Machine Elements and Manufacturing, 2003, 46(3): 960– 966.
[168] Sun D, Hu S, Shao X, Liu C. Global Stability of a Saturated Nonlinear PID Controller for Robot Manipulators [J]. IEEE Transactions on Control System Technology, 2009, 17(4): 892-899.
[169]冯勇,安澄全,李涛.采用双滑模平面减小一类非线性系统稳态误差[J].控制与决策, 2000, 15(3): 361-364.
[170]高为炳.变结构控制的理论及设计方法[M].北京:科学出版社. 1998.
[171] Okabayshi R, Furuta K. Design of Sliding Mode Control Systems with Constrained Inputs [C]// Proceedings of the 35th IEEE Conference on Decision and Control. Kobe, Japan, 1996: 3492-3497.
[172] Kothare M V, Campo P J, Morari M. A Unified Framework for Study of the Anti-Windup Design [J]. Automatica, 1994, 30(12): 1869-1883.
[173] Peng Y, Viranir D, Hanus R. Anti-windup, Bumpless, and Conditional Transfer Techniques for PID Controller [J]. IEEE Control System Magazine, 1996, 16(4): 48-57.
[174] Lu Y S, Chen J S. Design of a Global Sliding-Mode Controller for a Motor Drive with Bounded Control [J]. International Journal of Control, 1995, 62(5): 1001-1019.
[175] Davila J, Fridman L, Levant A. Second-Order Sliding-Mode Observer for Mechanical Systems [J]. IEEE Transactions on Automatic Control, 2005, 50(11): 1785-1789.
[176] Davila J, Fridman L, Poznyak A. Observation and Identification of Mechanical Systems via Second Order Sliding Modes [J]. International Journal of Control, 2006, 79(10): 1251-1262.
[177] Wu Q, Saif M. Robust Fault Diagnosis of a Satellite System Using a Learning Strategy and Second Order Sliding Mode Observer [J]. IEEE Systems Journal, 2010, 4(1): 112-121.
[178] Levant A. Homogeneity Approach to High-Order Sliding Mode Design [J].Automatica, 2005, 41(5): 823-830.
[179] Kobayashi S, Furuta K. Frequency Characteristics of Levant’s Differentiator and Adaptive Sliding Mode Differentiator [J]. International Journal of Systems Science, 2007, 38(10): 825-832.
[180] Shtessel Y B, Moreno J A, Plestan F, Fridman L M, Poznyak A S. Supper-twisting Adaptive Sliding Mode Control: A Lyapunov Design [C]//Proceedings of the 48th IEEE Conference on Decision and Control, Atlanta, USA, 2010: 5109-5112.
[181]俞立.鲁棒控制—线性矩阵不等式处理方法[M].北京:清华大学出版社, 2002.
[182]刘智平,周凤歧,周军.具有参数不确定性的飞行器的变结构姿态控制[J].宇航学报, 2007, 28(1): 43-48.
[183]张友安,王宏然,程继红.应用动态逆和三时标分离的飞航导弹过载控制离散化设计[J].吉林大学学报(工学版), 2006, 36(6): 1008-1013.
[184] Singh S N, Steinberg M L, Page A B. Nonlinear Adaptive and Sliding Mode Flight Path Control of F/A-18 Model [J]. IEEE Transactions on Aerospace and Electronic Systems, 2003, 39(4): 1250-1262.
[185] Levant A. Non-Homogeneous Finite-Time-Convergent Differentiator. Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference. Shanghai, P.R. China, December 16-18, 2009: 8399-8404.
[186] Dorsett K M, Mehl D R. Innovative Control Effectors (ICE), Final Report for September 1994-January 1996, Wright Laboratory, Air Force Material Command, WL-TR-96-3043, January 1996.
[187] Jovan D. BoSkovic, Sai-Ming Li, and Raman K. Mehra. Study of an Adaptive Reconfigurable Control Scheme for Tailless Advanced Fighter Aircraft (TAFA) in the Presence of Wing Damage.
[188]杨晖.先进重构飞行控制技术和方法研究[J].飞行力学, 2001, 19(4): 11-14.
[189] http://www.defence.org.cn/article-1-61696.html
[190]Willard J. Harris. X-36 Tailless Agility Aircraft Subsystems Integration[C]// Proceedings of the AIAA Guidance, Navigation, and Control Conference, AIAA 97-5505, 1997.
[191] http://www.airforce-technology.com/projects/x-45-ucav/
[192] Chen W H. Nonlinear Disturbance Observer Enhanced Dynamic Inversion Control [J]. AIAA Journal of Guidance, Control, and Dynamic Systems, 2003, 26(1): 161-166.
[193]陈谋,姜长生,吴庆宪.基于干扰观测器的一类不确定非线性系统鲁棒H∞控制[J].控制理论与应用,2006,23(4): 611-615.
[194] Reiner J, Balas G J, Garrard, W L. Flight Control Design Using Robust DynamicInversion and Time-scale Separation [J]. Automatica, 1996, 32(11): 1493–1504.
[195] Boskovic J D, Li S M, Raman K M. Robust Tracking Control Design for Spacecraft under Control Input Saturation [J]. AIAA Journal of Guidance, Control, and Dynamics, 2004, 27 (4): 627-633.
[196] Hess R A, Vetter T K, Wells S R. Design and Evaluation of a Damage Tolerant Flight Control System[C]//Proceedings of AIAA Guidance, Navigation, and Control Conference and Exhibit, Providence, Rhode Island, 2004: 1-21.
[197] Shen Y J, Xia X H. Semi-Global Finite-Time Observer for Nonlinear Systems [J]. Automatica, 2008, 44(12): 3152-3156.
[198] Bhat S, Bernstein D S. Finite-Time Stability of Continuous Autonomous Systems [J]. SIAM Journal on Control and Optimization, 2000, 38(3): 751-766.
[199] Bhat S, Bernstein D S. Finite Time Stability of Homogeneous Systems [C]//Proceedings of American Control Conference, Albuquerque, New Mexico, 1997: 602-609.
[200] Bhat S, Bernstein D S. Geometric Homogeneity with Applications to Finite-Time Stability [J]. Math. Control Signals Systems, 2005, 17(2): 101-127.
[201]李世华,丁世宏,田玉平.一类二阶非线性系统的有限时间状态反馈镇定方法[J].自动化学报, 2007, 33(1): 101-104.
[202] Zhang H, Wang X, Han D. Dual-Quaternion-Based Variable Structure Control: A New Approach and Application [C]//Proceedings of 2010 International Conference on Intelligent Robotics and Applications, Shanghai, China, 2010: 75-86.
[203] Athans M, Falb P L. Optimal Control: An Introduction to the Theory and Its Applications [M], New York: McGraw-Hill. 1966.
[204] Bhat S P, Berstein D S. Continuous Finite-Time Stabilization of the Translation and Rotational Double Integrator [J]. IEEE Transaction on Automatic Control, 1998, 43(5): 678-682.
[205] Rekasius Z V. An Alternate Approach to the Fixed Terminal Point Regulator Problem [J]. IEEE Transaction on Automatic Control, 1964, 9(3): 290-292.
[206] Bhat S P, Berstein D S. Geometric Homogeneity with Applications to Finite Time Stability [J]. Math. Control Signals Systems, 2005, 17(2): 101-127.
[207] Huang X, Lin W, Yang B, Global Finite-Time Stabilization of a Class of Uncertain Nonlinear Systems [J]. Automatica, 2005, 41(5): 881-888.
[208]王新华,陈增强,袁著祉.全程快速非线性跟踪-微分器[J].控制理论与应用,2003, 12(6): 875-878.
[209] Qian C, Lin W. A Continuous Feedback Approach to Global Strong Stabilization of Nonlinear Systems [J]. IEEE Transactions on Automatic Control, 2001, 46(7): 1061-1079.
[210] Bhat S P, Bernstein D S. Finite-Time Stability of Continuous AutonomousSystems [J]. SIAM Journal on Control Optimization, 2000, 38(3): 751-766.
[211] Qian C, Lin W. Non-Lipschitz Continuous Stabilizers for Nonlinear Systems with Uncontrollable Unstable Linearization [J]. Systems & Control Letters, 2001, 42(3): 185-200.