非仿射非线性不确定系统的自适应模糊控制研究及应用
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摘要
非仿射非线性系统广泛存在于现实生活中,考虑到实际系统通常具有不确定性,控制非仿射非线性不确定系统是一项创新而又富有挑战性的课题,具有重要的理论意义和应用价值。围绕这一课题,基于模糊逻辑系统的万能逼近特性,系统化地研究了几类非仿射非线性系统的自适应模糊控制方法。
针对一类单输入单输出非仿射非线性不确定系统,分别设计自适应模糊状态反馈控制器和输出反馈控制器。在系统状态可测的情况下,用模糊逻辑系统逼近未知函数,模糊参数采用σ自适应律,给出参数的有界性证明,引入鲁棒控制项来消除模糊逻辑系统的逼近误差和系统的外界干扰,使得闭环系统跟踪误差收敛到零。为了抑制控制的抖振性,鲁棒控制项中引入双曲正切函数,设计了与之匹配的自适应参数调整律,并证明了闭环系统所有信号一致最终有界,跟踪误差收敛到零的一个邻域。将算法应用到Duffing-Holmes混沌系统、Sprott电路系统、Genesio混沌系统,验证了算法的有效性。在系统状态不可测的情况下,构造线性误差观测器估计系统输出误差和系统状态,利用估计状态变量和估计输出误差变量设计自适应控制律,并证明了闭环系统的稳定性,控制性能在Duffing-Holmes混沌系统的应用中得到验证。
针对一类具有严格反馈形式的非仿射非线性系统设计基于Backstepping方法的自适应模糊控制律,仅要求模糊逻辑系统的逼近误差范数有界,设计自适应律时只考虑对未知参数范数的估计值进行在线调整,这样减少在线调整参数的数目,采用自适应鲁棒控制项消除逼近误差和外界干扰。证明了闭环系统在Lyapunov意义下的稳定性,并将该方法应用到Chua’s电路系统和R?ssler混沌系统中来验证算法的有效性。
针对一类严格反馈型多输入多输出非仿射非线性系统设计一种自适应模糊控制器,该系统由多个互联子系统组成,针对每个子系统构造Lyapunov函数以设计相应的控制律,最后设计整个系统的Lyapunov函数,从而保证闭环系统所有信号一致最终有界,跟踪误差收敛到零的一个邻域。将算法应用到Lorenz系统、永磁同步电动机系统、Lü系统、Liu系统以及超混沌R?ssler系统的控制中,并通过仿真分析验证了算法的有效性。
针对非仿射非线性时滞系统提出一种自适应模糊控制算法,通过构造适当的Lyapunov- Krasovskii泛函有效消除系统的时滞项,利用双曲正切函数的连续性来解决补偿过程中产生的非线性余留项可能引起奇异性问题,并从理论上证明闭环系统的稳定性。将带时滞的Rssler混沌系统作为仿真对象,进行控制律设计,给出仿真结果,验证算法的有效性。
最后,针对控制律设计中的参数选择问题,采用最佳保留遗传算法来选择参数值,将跟踪误差、模糊系统复杂性、控制输入的抖振性作为目标函数,设计相应的遗传算子,得到较优的设计参数,并用数值算例验证算法的有效性。
Nonaffine nonlinear systems widely exist in real world. Taking into account that the actual system is often uncertain, how to control the nonaffine nonlinear uncertain systems is an innovative and challenging subject and has important theoretical and practical value. To solve this problem, based on the universal approximation properties of fuzzy logic system (FLS), this thesis systematically studies a series of adaptive fuzzy control strategies for several types of nonaffine nonlinear systems.
Adaptive state-feedback and output-feedback fuzzy controllers are developed for a class of single input single output (SISO) nonaffine nonlinear uncertain systems. In the situation that the system states are observable, a fuzzy logic system is employed to approximate the unknown nonlinearity, the adjustable parameters in FLS are updated byσadaptive law and the proof of boundedness of parameters is given. A robust control term is introduced to compensate the approximation error and disturbances to make the tracking error converge to zero. In order to avoid chattering of the control input,a tanh function is used in robust term and the corresponding adaptive law is redesigned. The proposed controller guarantees that all the signals in the closed-loop system are bounded and the tracking error eventually converges to a small neighborhood of zero. The developed design scheme is applied to Duffing-Holmes system, Genesio system and Sprott circuit chaotic system. Simulation results demonstrate the effectiveness of the proposed approach. In additon, it is assumed that the system states are unavailable, then a linear error observer is employed to estimate output errors and states. An adaptive controller is designed by using the observed values of errors and states, so that the whole closed loop system is stable in the sense of Lyapunov. Duffing-Holmes chaotic system is used to emphasize the effectiveness of the approach.
Based on backstepping approach, a robust adaptive fuzzy control scheme is presented for a class of strict-feedback nonaffine nonlinear systems. Approximation errors of fuzzy systems are only required norm-bounded, and the online computation quantity is reduced by tuning estimations of the unknown bounds online. An additional adaptive term is employed to compensation approximation errors and disturbances. The stability of the whole closed loop system is proved via Lyapunov method. Chua’s circuit sytem and R?ssler chaotic system is presented to illustrate the feasibility and effectiveness of the proposed control technique.□
An adaptive fuzzy control schemes is proposed for a class of multi-input multi-output (MIMO) nonaffine nonlinear systems in block-triangular forms. The MIMO systems consist of interconnected subsystems, Lyapunov function is constructed for each subsystem to design the corresponding control law. Finally, Lyapunov function of the whole system is designed so that the all the signals in the closed-loop system are bounded and the tracking error eventually converges to a small neighborhood of zero. The developed design scheme is applied to Lorenz system, permanent-magnet synchronous motor system, Lüsystem, Liu system and hyperchaotic R?ssler system. Simulation results demonstrate the effectiveness of the proposed approach.
An adaptive fuzzy control schemes is proposed for a class of strict-feedback nonaffine nonlinear systems with time delays, the unknown time delays are compensated for using appropriate Lyapunov-Krasovskii functionals, the singularity generated in the process of compensation is overcome by the using of tanh function. The proposed controller guarantees that all closed-loop signals remain bounded. R?ssler chaotic system with time delay is given to illustrate the design procedure and performance of the proposed method.
Parameter selection is another important problem for controller design. Thus, in the last part of the thesis, taking the complexity of FLS, tracking error and control oscillation as object functions, an elitist preserved genetic algorithm is employed to search for the optimum parameters by designing corresponding genetic operators. A simulation example is presented to illustrate the feasibility and effectiveness of the proposed control technique.
针对一类单输入单输出非仿射非线性不确定系统,分别设计自适应模糊状态反馈控制器和输出反馈控制器。在系统状态可测的情况下,用模糊逻辑系统逼近未知函数,模糊参数采用σ自适应律,给出参数的有界性证明,引入鲁棒控制项来消除模糊逻辑系统的逼近误差和系统的外界干扰,使得闭环系统跟踪误差收敛到零。为了抑制控制的抖振性,鲁棒控制项中引入双曲正切函数,设计了与之匹配的自适应参数调整律,并证明了闭环系统所有信号一致最终有界,跟踪误差收敛到零的一个邻域。将算法应用到Duffing-Holmes混沌系统、Sprott电路系统、Genesio混沌系统,验证了算法的有效性。在系统状态不可测的情况下,构造线性误差观测器估计系统输出误差和系统状态,利用估计状态变量和估计输出误差变量设计自适应控制律,并证明了闭环系统的稳定性,控制性能在Duffing-Holmes混沌系统的应用中得到验证。
针对一类具有严格反馈形式的非仿射非线性系统设计基于Backstepping方法的自适应模糊控制律,仅要求模糊逻辑系统的逼近误差范数有界,设计自适应律时只考虑对未知参数范数的估计值进行在线调整,这样减少在线调整参数的数目,采用自适应鲁棒控制项消除逼近误差和外界干扰。证明了闭环系统在Lyapunov意义下的稳定性,并将该方法应用到Chua’s电路系统和R?ssler混沌系统中来验证算法的有效性。
针对一类严格反馈型多输入多输出非仿射非线性系统设计一种自适应模糊控制器,该系统由多个互联子系统组成,针对每个子系统构造Lyapunov函数以设计相应的控制律,最后设计整个系统的Lyapunov函数,从而保证闭环系统所有信号一致最终有界,跟踪误差收敛到零的一个邻域。将算法应用到Lorenz系统、永磁同步电动机系统、Lü系统、Liu系统以及超混沌R?ssler系统的控制中,并通过仿真分析验证了算法的有效性。
针对非仿射非线性时滞系统提出一种自适应模糊控制算法,通过构造适当的Lyapunov- Krasovskii泛函有效消除系统的时滞项,利用双曲正切函数的连续性来解决补偿过程中产生的非线性余留项可能引起奇异性问题,并从理论上证明闭环系统的稳定性。将带时滞的Rssler混沌系统作为仿真对象,进行控制律设计,给出仿真结果,验证算法的有效性。
最后,针对控制律设计中的参数选择问题,采用最佳保留遗传算法来选择参数值,将跟踪误差、模糊系统复杂性、控制输入的抖振性作为目标函数,设计相应的遗传算子,得到较优的设计参数,并用数值算例验证算法的有效性。
Nonaffine nonlinear systems widely exist in real world. Taking into account that the actual system is often uncertain, how to control the nonaffine nonlinear uncertain systems is an innovative and challenging subject and has important theoretical and practical value. To solve this problem, based on the universal approximation properties of fuzzy logic system (FLS), this thesis systematically studies a series of adaptive fuzzy control strategies for several types of nonaffine nonlinear systems.
Adaptive state-feedback and output-feedback fuzzy controllers are developed for a class of single input single output (SISO) nonaffine nonlinear uncertain systems. In the situation that the system states are observable, a fuzzy logic system is employed to approximate the unknown nonlinearity, the adjustable parameters in FLS are updated byσadaptive law and the proof of boundedness of parameters is given. A robust control term is introduced to compensate the approximation error and disturbances to make the tracking error converge to zero. In order to avoid chattering of the control input,a tanh function is used in robust term and the corresponding adaptive law is redesigned. The proposed controller guarantees that all the signals in the closed-loop system are bounded and the tracking error eventually converges to a small neighborhood of zero. The developed design scheme is applied to Duffing-Holmes system, Genesio system and Sprott circuit chaotic system. Simulation results demonstrate the effectiveness of the proposed approach. In additon, it is assumed that the system states are unavailable, then a linear error observer is employed to estimate output errors and states. An adaptive controller is designed by using the observed values of errors and states, so that the whole closed loop system is stable in the sense of Lyapunov. Duffing-Holmes chaotic system is used to emphasize the effectiveness of the approach.
Based on backstepping approach, a robust adaptive fuzzy control scheme is presented for a class of strict-feedback nonaffine nonlinear systems. Approximation errors of fuzzy systems are only required norm-bounded, and the online computation quantity is reduced by tuning estimations of the unknown bounds online. An additional adaptive term is employed to compensation approximation errors and disturbances. The stability of the whole closed loop system is proved via Lyapunov method. Chua’s circuit sytem and R?ssler chaotic system is presented to illustrate the feasibility and effectiveness of the proposed control technique.□
An adaptive fuzzy control schemes is proposed for a class of multi-input multi-output (MIMO) nonaffine nonlinear systems in block-triangular forms. The MIMO systems consist of interconnected subsystems, Lyapunov function is constructed for each subsystem to design the corresponding control law. Finally, Lyapunov function of the whole system is designed so that the all the signals in the closed-loop system are bounded and the tracking error eventually converges to a small neighborhood of zero. The developed design scheme is applied to Lorenz system, permanent-magnet synchronous motor system, Lüsystem, Liu system and hyperchaotic R?ssler system. Simulation results demonstrate the effectiveness of the proposed approach.
An adaptive fuzzy control schemes is proposed for a class of strict-feedback nonaffine nonlinear systems with time delays, the unknown time delays are compensated for using appropriate Lyapunov-Krasovskii functionals, the singularity generated in the process of compensation is overcome by the using of tanh function. The proposed controller guarantees that all closed-loop signals remain bounded. R?ssler chaotic system with time delay is given to illustrate the design procedure and performance of the proposed method.
Parameter selection is another important problem for controller design. Thus, in the last part of the thesis, taking the complexity of FLS, tracking error and control oscillation as object functions, an elitist preserved genetic algorithm is employed to search for the optimum parameters by designing corresponding genetic operators. A simulation example is presented to illustrate the feasibility and effectiveness of the proposed control technique.
引文
[1] Pashilkar A A. Adaptive nonlinear neural controller for aircraft under actuator failures [J]. Journal of Guidance, Control, and Dynamics. 2007, 30(3): 834-847.
[2]朱亮.空天飞行器不确定非线性鲁棒控制[D].南京:南京航空航天大学,2006.
[3]丁青青,王树民,郭静波. HVDC非仿射非线性系统的定电流定电压控制[J].清华大学学报(自然科学版), 2004, 44(10): 1325-1328.
[4]汤洪海,李春文.基于非仿射非线性模型的AC/DC系统H∞鲁棒控制器设计[J].自动化学报, 2007, 33(7): 709-713.
[5] Mutha R K, Cluett W R, Penlidis A. Nonlinear model-based predictive control of control nonaffine systems [J]. Automatica, 1997, 33(5): 907-913.
[6] Krstic M, Kanellakopoulos I, Kokotovic P V. Nonlinear and Adaptive control design [M]. Wiley, New York, 1995.
[7]冯纯伯,费树岷.非线性控制系统分析与设计[M].第二版,北京:电子工业出版社,1997.
[8] Chiasson J. A New Approach to Dynamic Feedback Linearization Control of an Induction Motor [J]. IEEE Transations on Automatic Control, 1998, 43(3): 391-396.
[9] Hamzaoui A, Essounbouli N, Benmahammed K, et al. State observer based robust adaptive fuzzy controller for nonlinear uncertain and perturbed systems [J]. IEEE Trans. Systems, Man Cybernetics-Part B: Cybernetics, 2004, 34(2): 942-950.
[10] Park J H, Park G T, Kim S H, et al. Direct adaptive self-structuring fuzzy controller for nonaffine nonlinear system [J]. Fuzzy Sets and Systems. 2005, 153 (3), 429-445.
[11] Chen W S. Adaptive Backstepping dynamic surface control for systems with periodic disturbances using neural networks [J]. IET Control Theory and Applications, 2009, 3(10): 1383-1394.
[12] Ge S S, Wang C. Adaptive neural control of uncertain MIMO nonlinear systems [J]. IEEE Transactions on Neural Networks, 2004, 15(3): 674-692.
[13]王立新著,王迎军译.模糊系统与模糊控制[M].北京:清华大学出版社,2003.
[14]胡海岩,王在华.论迟滞与时滞[J],力学学报, 2010, 42(7): 740-746.
[15] Jiang X F, Han Q L. New stability criteria for linear systems with interval time-varying delay [J]. Automatica, 2008, 44(10): 2680-2685.
[16] Liu Y J, Wang W. Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems[J]. Information Sciences, 2007, 177 (18): 3901-3917.
[17] Leu Y G, Wang W Y, Lee T T. Observer-based direct adaptive fuzzy-neural control for nonaffine nonlinear systems [J]. IEEE Transactions on neural networks, 16(4): 853-861.
[18] Lin W. Time-varying feedback control of nonaffine nonlinear systems without drift [J]. Systems & Control Letters, 1996, 29(2): 101-110.
[19] Schiff S J, Jerger K, Duong D H, et al. Controlling chaos in the brain [J]. Nature, 1994, 370(2): 615-620.
[20] Petrov V, Gaspar V, Masere J, et al. Controlling chaos in the Belousov-Zhabotinsky reaction [J]. Nature, 1993, 361:240-243.
[21]黄润生.混沌及其应用[M].武汉:武汉大学出版社, 2003.
[22] Li C D, Liao X F, Wang K W. Chaotic lag synchronization of coupled time-delayed systems and its applications in secure communication [J]. Physica D: Nonlinear Phenomena, 2004, 194 (3-4): 187-202.
[23] Gámez-Guzmán L, Crue-Hernández C, López-Gutiérrez R M, et al. Synchronization of Chua’s circuits with multi-scroll attracors: application to communication [J]. Communications in Nonlinear Science and Numerical Simulation, 2009, 14(6): 2765-2775.
[24] Wu T Y, Chen M S. Chaos control of the modified Chua’s circuit system [J]. Physica D: Nonlinear Phenomena, 2002, 164(1-2): 53-58.
[25] Botmart T C, Niamsup P. Adaptive control and synchronization of the perturbed Chua’s system [J]. Mathematics and Computers in Simulation, 2007, 75(1-2): 37-55.
[26] Mahmoud G M, Mohamed A A, Aly S A. Strange attractors and chaos control in periodically forced complex Duffing’s oscillators [J]. Physica A: Statistical Mechanics and its Applications, 2001, 292(1-4): 193-206.
[27] Qi G Y, Chen Z Q, Yuan Z Z. Model-free control of affine chaotic systems [J]. Physics Letters A, 2005, 344(2-4): 189-202.
[28] Bagheri A, Moghaddam J J. Decoupled adaptive neuro-fuzzy (DANF) sliding mode control system for Lorenz chaotic problem [J]. Expert Systems with Applications, 2009, 36(2): 6062-6068.
[29] Park C W, Lee C H, Park M. Design of an adaptive fuzzy model based controller for chaotic dynamics in Lorenz systems with uncertainty [J]. Information Sciences, 2002, 147(1-4): 245-266.
[30] Rafikov M, Balthazar J M. On an optimal control design for R?ssler system [J]. Physics LetterA, 2004, 333(3-4): 241-245.
[31] Sun J T, Zhang Y P. Impulsive control of R?ssler system [J]. Physics Letter A, 2003, 306(5-6): 306-312.
[32] Zadeh L A. Fuzzy sets [J]. Information and Control, 1965, 8(3): 338-353.
[33] Zadeh L A. Outline of a new approach to the analysis of complex systems and decision processes [J]. IEEE Trans. Syst. Man, Cybern, 1973, 3(1): 28-44.
[34] Wang L X. Fuzzy systems are universal approximators [C]. Proceeding of IEEE International Conf. on Fuzzy Systems, San Diego, USA, 1992: 1163-1170.
[35] Kanellakopoulos I, Kokotovic P V, Morse A S. Systematic design of adaptive controllers for feedback linearizable systems [J], IEEE Trans. Automat Contr., 1991, 36(11):1241-1253.
[36] Jiang Z P, Hill D J. A robust adaptive Backstepping scheme for nonlinear systems with unmodeled dynamics [J]. IEEE Trans Automat Contr., 1999, 44(9): 1705-1711.
[37] Li J H, Lee P M. A neural network adaptive controller design for free-pitch-angle diving behavior of an autonomous underwater vehicle [J]. Robotics and Autonomous Systems, 2005, 52(2-3): 132-144.
[38] Li T S, Yang Y S, Hong B G, et al. A robust adaptive nonlinear control approach to ship straight-path tracking design [C], American control conference, Portland, 2005: 4016-4021.
[39] Marquez-Martinez L A, Moon C H. Input-output feedback linearization of time-delay systems [J]. IEEE Trans. Automatic Control, 2004, 49(5): 781-785.
[40] Ma X, Tao G. Adaptive actuator compensation control with feedback linearizaiton [J]. IEEE Trans. Automatic Control, 2000, 45(9): 1705-1710.
[41] Rugh W J, Shamma J S. Research on gain scheduling [J]. Automatica, 2000, 36(10): 1401- 1425.
[42] Tan S H, Hang C C, Chai J S. Gain scheduling: from conventional to neural-fuzzy [J]. Automatica, 1997, 33(3): 411-419.
[43] Utkin V I. Variable Structure systems with sliding modes [J]. IEEE Trans. Automatic Control, 1977, 22(2): 212-222.
[44]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): 407-418.
[45] Jiang A P, Nijmeijer H. Tracking control of mobile robots: A case study in Backstepping [J]. Automatica, 1997, 33(7): 1393-1399.
[46] Jiang Z P. A combined Backstepping and small-gain approach to adaptive output feedbackontrol [J]. Automatica, 1999, 35(6): 1131-1139.
[47] Cho Y W, Prak C W, Park M. An indirect model reference adaptive fuzzy control for SISO Takagi-Sugeno model [J]. Fuzzy Sets and Systems, 2002, 131(2), 197-215.
[48] Phan P A, Gale T J. Direct adaptive fuzzy control with a self-structuring algorithm [J]. Fuzzy Sets and Systems, 2008, 159(8): 871-899.
[49] Leu Y G, Lee T T, Wang W Y. Observer-based adaptive fuzzy-neural control for unknown nonlienar dynamical system [J]. IEEE Trans. Systems, Man Cybernetics-Part B: Cybernetics, 1999, 29(5): 583-591.
[50] Wang W Y, Leu Y G, Lee T T. Out-feedback control of nonlinear systems using direct adaptive fuzzy-neural controller [J]. Fuzzy Sets and Systems, 2003, 140(2): 341-358.
[51] Park J H, Park G T, Kim. S.H, Kim S H, et al. Output-feedback control of uncertain nonlinear systems using a self-structuring adaptive fuzzy observer [J]. Fuzzy Sets and Systems, 2005, 151(1): 21-42.
[52] Hamzaoui A, Essounbouli N, Benmahammed K, et al. State observer based robust adaptive fuzzy controller for nonlinear uncertain and perturbed systems [J]. IEEE Trans. Systems, Man Cybernetics-Part B: Cybernetics, 2004, 34(2): 942-950.
[53] Boulkroune A, Tadjine M, Saad M M’, et al. How to design a fuzzy adaptive controller based on observers for uncertain affine nonlinear systems [J]. Fuzzy Sets and Systerms, 2008, 159(8) 926-948.
[54] Yang Y S, Feng G, Ren J S. A combined Backstepping and small-gain approach to robust adaptive fuzzy control for strict-feedback nonlinear system [J]. IEEE Trans. Systems. Man, Cybernetics–Part A: System and Humans, 2004, 34(3): 406-420.
[55] Taylor D G, Kokotovic P V, Marino R, et al. Adaptive regulation of nonlinear systems with unmodeled dynamics [J]. IEEE Trans. Automatic Control, 1989, 34(4): 405-412.
[56] Pomet J B, Praly L. Adaptive nonlinear regulation: estimation from the Lyapunov equation. IEEE Trans. Automatic Control, 1992, 37(6): 729-740.
[57] Barmish B R, Leitmann G. On ultimate boundedness control of uncertain systems in the absence of matching assumptions [J]. IEEE Trans. Automatic Control, 1982, 27(1): 153-158.
[58] Corless M, Leitmann G. Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems [J]. IEEE Trans. Automatic Control, 1981, 26(5): 1139-1144.
[59] Fabri S, Kadirkamanathan V. Dynamic structure neural networks for stable adaptive control of nonlinear systems. IEEE Trans. Neural Networks, 1996, 7(5): 1151-1167.
[60] Wang L X. Stable adaptive fuzzy control of nonlinear systems. IEEE Trans. Fuzzy System, 1993, 1(2): 146-155.
[61] Kanellakopoulos I, Kokotovic P V, Morse A S. Systematic design of adaptive controller for feedback linearizable systems [J]. IEEE Trans. Automatic Control, 1991, 36(11): 1241-1253.
[62] Marino R, Tomei P. Global adaptive output-feedback control of nonlinear systems, part II: nonlinear parameterization [J]. IEEE Trans. Automatic Control, 1993, 38(1): 33-49.
[63] Wang W Y, Chan M L, Lee T T, et al. Adaptive fuzzy control for strict-feedback canonical nonlinear systems with tracking performance [J]. IEEE Trans. Systems, Man Cybernetics-Part B: Cybernetics, 2000, 30(6): 878-885.
[64] Yao B, Tomizuka M. Adaptive robust control of SISO nonlinear systems in a semi-strict feedback form [J]. Atutomatica, 1997, 33(5): 893-900.
[65] Ge S S, Wang C. Adaptive control of uncertain Chua’s circuits [J]. IEEE Trans. On Circuits Systems-I: Fundamental Theory and Applications, 2000, 47(9): 1397-1402.
[66] Chang Y C. Intelligent robust tracking control for a class of uncertain strict-feedback nonlinear systems [J]. IEEE Trans. Systems, Man Cybernetics-Part B: Cybernetics, 2000, 39(1): 142-155.
[67] Zhou S S, Feng G, Feng C B. Robust control for a class of nonlinear systems: adaptive fuzzy approach based on Backstepping [J]. Fuzzy Sets and Systems, 2005, 151(1): 1-20.
[68] Li Y H, Qiang S, Zhang X Y, et al. Robust and adaptive Backstepping control for nonlinear systems using RBF neural networks [J]. IEEE Trans. Neural Networks, 2004, 15(3): 693-701.
[69] Ge S S, Wang C. Adaptive NN control of uncertain nonlinear pure-feedback systems [J]. Automatica, 2002, 38(4): 671-682.
[70] G S S, Wang C. Direct adaptive NN control of a class of nonlinear systems [J]. IEEE Trans. Neural Networks, 2002, 13(1): 214-221.
[71] Chen W S, Jiao L C. Adaptive tracking for periodically time-varying and nonlinear parameterized systems using multilayer neural networks [J]. IEEE Trans. Neural Networks, 2010, 21(2): 345-351.
[72] Chen B, Liu X P, Liu K F, et al. Direct adaptive fuzzy control of nonlinear strict-feedback systems [J]. Automatica, 2009, 45(6): 1530-1535.
[73] Wang M, Chen B, Dai S L. Direct adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear systems [J]. Fuzzy Sets and Systems, 2007, 158(24): 2655-2670.
[74] Ho H F, Wong Y K, Rad A B. Adaptive fuzzy approach for a class of uncertain nonlinear systems in strict-feedback form [J]. ISA Transactions, 2008, 47(3): 286-299.
[75] Yang Y S, Zhou C J. Robust adaptive fuzzy tracking control for a class of perturbed strict- feedback nonlinear systems via small-gain approach [J]. Infromation Sciences, 2005, 170(2-4): 211-234.
[76] Tong S C, Li Y M, Shi P. Fuzzy adaptive Backstepping robust control for SISO nonlinear system with dynamic uncertains [J]. Infromation Sciences, 2009, 179(9): 1319-1332.
[77] Tong S C, He X L, Li Y M, et al. Adaptive fuzzy Backstepping robust control for uncertain nonlinear systems based on small-gain approach [J]. Fuzzy Sets and Systems, 2010, 161(6): 771-796.
[78] Yang Y S, Zhou C J. Adaptive fuzzy H∞stabilization for strict-feedback canonical nonlinear systems via Backstepping and small-gain approach [J]. IEEE Trans. Fuzzy Systems, 2005, 13(1): 104-114.
[79] Zhang T P, Ge S S. Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form [J]. Automatica, 2008, 44(7): 1895-1903.
[80] Wang D, Huang J. Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form [J]. IEEE Trans. Neural Networks, 2005, 16(1): 195-202.
[81] Ge S S, Wang J. Robust adaptive neural control for a class of perturbed strict-feedback nonlinear systems [J]. IEEE Trans. Neural Networks, 2002, 13(6): 1409-1419.
[82] Li J, Chen W S, Li J M, et al. Adaptive NN output-feedback stabilization for a class of stochastic nonlinear strict-feedback systems [J]. ISA Transactions, 2009, 48(4): 468-475.
[83] Tong S C, Li Y M. Observer-based fuzzy adaptive control for strict-feedback nonlinear systems [J]. Fuzzy Sets and Systems, 2009, 160(12): 1749-1764.
[84] Chen B, Liu X P, Tong S C. Adaptive fuzzy output tracking control of MIMO nonlinear uncertain systems [J]. IEEE Trans. Neural Networks, 2007, 15(2): 287-300.
[85] Liu Y J, Wang W, Tong S C, et al. Robust Adaptive tracking control for nonlinear systems based on bounds of fuzzy approximation parameters [J]. IEEE Trans. Systems. Man, Cybernetics–Part A: System and Humans, 2010, 40(1): 170-184.
[86] Li T S, Tong S C, Feng G. A novel robust adaptive-fuzzy-tracking control for a class of nonlinear multi-input/multi-output systems [J]. IEEE Trans. Fuzzy Systems, 2010, 18(1): 150-160.
[87] Chen B, Liu X P. Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by Backstepping and application to chemical processes [J]. IEEE Trans. Fuzzy Systems, 2005,13(6): 832-847.
[88] Chen B, Tong S C, Liu X P. Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by Backstepping approach [J]. Fuzzy Sets and Systems, 2007, 158(10): 1097-1125.
[89] Zou A M, Hou Z G, Tan M. Adaptive control of a class of nonlinear pure-feedback systems using fuzzy Backstepping approach [J]. IEEE Trans. Fuzzy Systems, 2008, 16(4): 886-896.
[90] Yoo S J, Park J B, Choi Y H. Adaptive neural control for a class of strict-feedback nonlinear systems with state time delays [J]. IEEE Trans. Neural Networks, 2009, 20(7): 1209-1215.
[91] Ge S S, Hong F, Lee T H. Adaptive neural network control of nonlinear systems with unknown time delays [J]. IEEE Trans. Automatic Control, 2003, 48(11): 2004-2010.
[92] Ge S S, Tee K P. Approximation-based control of nonlinear MIMO time-delay systems [J]. Automatica, 2007, 43(1): 31-43.
[93] Wang M, Chen B, Liu X P, et al. Adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear time-delay systems [J]. Fuzzy Sets and Systems, 2008, 159(8): 949-967.
[94] Wang M, Chen B, Shi P. Adaptive neural control for a class of perturbed strict-feedback nonlinear time-delay systems [J]. IEEE Trans. Systems, Man Cybernetics-Part B: Cybernetics, 2008, 38(3): 721-730.
[95] Chen B, Liu X P, Liu K F, et al. Fuzzy-approximation-based adaptive control of strict-feedback nonlinear systems with time delays [J]. IEEE Trans. Fuzzy Systems, 2010, 18(5): 883-892.
[96] Chen B, Liu X P, Liu K F, et al. Novel adaptive neural control design for nonlinear MIMO time-delay systems [J]. Automatica, 2009, 45(6): 1554-1560.
[97] Hua C C, Feng G, Guan X P. Robust controller design of a class of nonlinear time delay systems via backstepping method. Automatic, 2008, 44(2): 567-573.
[98] Chen B, Liu X P, Liu K F, et al. Direct adaptive fuzzy control for nonlinear systems with time-varying delays [J]. Informaiton Sciences, 2010, 180(5): 776-792.
[99]沈启坤,张天平,钱厚斌.一类非仿射非线性系统的自适应模糊控制[J].电机与控制学报,2006, 10(6): 592-596.
[100]胡慧,刘国荣,郭鹏等.基于观测器的一类非仿射非线性系统的自适应神经网络H∞跟踪控制[J],信息与控制, 2009, 38(4): 468-472.
[101] Hovakimyan N, Nardi F, Calise A J. A novel error observer-based adaptive output feedback approach for control of uncertain systems [J]. IEEE Trans. Automatic Control, 2002, 47(8): 1310-1314.
[102] Yang B J, Calise A J. Adaptive control of a class of nonaffine systems using neural networks [J]. IEEE Trans. Neural Networks, 2007, 18(4): 1149-1159.
[103] Teo J, How J P, Lavretsky E. Proportional-integral controllers for minimum-phase nonaffine -in-control systems [J]. IEEE Trans. Automatic control, 2010, 55(6): 1477-1483.
[104] Zhao T. RBFN-based decentralized adaptive control of a class of large-scale non-affine nonlinear sytems [J]. Neural Comput & Applic., 2008, 17(4): 357-364.
[105] Boulkroune A, Tadjine M, M’Saad M, et al. Adaptive fuzzy control for non-affine systems with zero dynamics [J]. International Journal of Systems Science, 2009, 40(4): 367-382.
[106] Tee K P, Ge S S, Tay E H. Adaptive neural network control for helicopters in vertical flight [J]. IEEE Trans. Control Systems Technology, 2008, 16(4): 753-762.
[107] Du H B, Chen X C. NN-based output feedback adaptive variable structure control for a class of non-affine nonlinear systems: A nonseparation principle design [J]. Neurocomputing, 2009, 72(2-9): 2009-2016.
[108] Labiod S, Guerra T M. Adaptive fuzzy control of a class of SISO nonaffine nonlinear systems [J]. Fuzzy Sets and Systems, 2007, 158(10): 1126-1137.
[109] Park J H, Park G T, et al. Direct adaptive self-structuring fuzzy controller for nonaffine nonlinear system [J]. Fuzzy Sets and Systems, 2005, 153 (3): 429-445.
[110] Park J H, Kim S H. Direct adaptive output-feedback fuzzy controller for a nonaffine nonlinear system [J]. IEE Proc.-Control Theory Appl., 2004, 151(1): 65-72.
[111] Ren B B, Ge S S, Su C Y, et al. Adaptive neural control for a class of uncertain nonlinear systems in pure-feedback form with hysteresis input [J]. IEEE Trans. Systems, Man Cybernetics-Part B: Cybernetics, 2009, 39(2): 431-443.
[112]杜红彬,邵惠鹤.一类非线性系统的自适应模糊神经网络控制[J].控制与决策, 2005, 20(4): 454-458.
[113]杜红彬,李绍军.一类纯反馈非仿射非线性系统的自适应神经网络变结构控制[J].系统工程与电子技术, 2008, 30(4): 723-726.
[114] Zou A M, Hou Z G, Tan M. Adaptive control of a class of nonlinear pure-feedback systems using fuzzy backstepping approach [J]. IEEE Trans. Fuzzy Systems, 2008, 16(4): 886-897.
[115]刘艳军,王伟.一类多变量非线性系统的自适应模糊控制[J].自动化学报, 2007, 33(11): 1163-1169.
[116] Liu Y J, Wang W. Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems [J]. Information Sciences, 2007, 177(18): 3901-3917.
[117] Liu Y J, Tong S C, Wang W. Adaptive fuzzy output tracking control for a class of uncertain nonlinear systems [J]. Fuzzy Sets and Systems, 2009, 160(19): 2727-2754.
[118] Wang M, Ge S S, Hong K S. Approximation-based adaptive tracking control of pure-feedback nonlinear systems with multiple unknown time-varying delays [J]. IEEE Trans. Neural Networks, 2010, 21(11): 1804-1816.
[119] Ren B B, Ge S S, Lee T H, et al. Adaptive neural control of SISO non-affine nonlinear time-delay systems with unknown hysteresis input [C], American control conference, Washington, USA, 2008: 4203-4208.
[120] Lin S C, Chen Y Y. Design of self-learning fuzzy sliding mode controllers based on genetic algorithms [J]. Fuzzy Sets and Systems, 1997, 86(2): 139-153.
[121] Alfaro-Cid E, McGookin E W, Murray-Smith D J. A comparative study of genetic operators for controller parameter optimization [J]. Control Engineering Pracctice, 2009, 17(1): 185-197.
[122] Cazarez-Castro N R, Aguilar L T, Castillo O. Fuzzy logic control with genetic membership function parameters optimization for the output regulation of a servomechanism with nonlinear backlash [J]. Expert Systems with Applications, 2010, 37(6): 4368-4378.
[123] Li R H, Zhang Y. Fuzzy logic controller based on genetic algorithms [J]. Fuzzy Sets and Systems, 1996, 83(1): 1-10.
[124] Onnen C, Babuska R, Kaymak U, et al. Genetic algorithms for optimization in predictive control [J]. 1997, 5(10): 1363-1372.
[125] Fleming P J, Purshouse R C. Evolutionary algorithms in control systems engineering: a survey [J]. Control Engineering Practices, 2002, 10(11): 1223-1241.
[126] Giordano V, Naso D, Turchiano B. Combining genetic algorithms and Lyapunov-based adaptive for online design of fuzzy controllers [J]. IEEE Trans. Systems, Man Cybernetics-Part B: Cybernetics, 2006, 36(5): 1118-1126.
[127] Ioannou P A, Sun J. Robust adaptive control [M]. Prentice-Hall, Englewood Cliffs, NJ, 1996.
[128] Polycarpou M M, Ioannou P A. A robust adaptive nonlinear control design [J]. Automatica, 1996, 32(3): 423-427.
[129] Ablay G. Sliding mode control of uncertain unified chaotic systems [J]. Nonlinear Analysis: Hybrid Systems, 2009, 3(4): 531-535.
[130] Zhou J, Er M J. Adaptive output control of a class of uncertain chaotic systems [J]. Systems & Control Letters, 2007, 56(6): 452-460.
[131] Lu Z, Shieh L S, Chen G R, et al. Adaptive feedback linearization control of chaotic systems viarecurrent high-order neural networks [J]. Information Sciences, 2006, 176(16): 2337-2354.
[132] Noroozi N, Roopaei M, Karimaghaee P, et al. Simple adaptive variable structure control for unknown chaotic systems [J]. Communications in Nonlinear Science and Nnmerical Simulaiton, 2010, 15(3): 707-727.
[133] Poursamad A, Davaie-Markazi A H. Robust adaptive fuzzy control of unknown chaotic systems [J]. Applied Soft Computing, 2009, 9(3): 970-976.
[134] Lin D, Wang X Y, Nian F Z, et al. Dynamic fuzzy neural networks modeling and adaptive backstepping tracking control of uncertain chaotic systems [J]. Neurocomputing, 2010, 73(16- 18): 2873-2881.
[135] Ting C S. An observer-based approach to controlling time-dealy chaotic systems via Takagi- sugeno fuzzy model [J]. Information Sciences, 2007, 177(20): 4314-4328.
[136] Qi G Y, Chen Z Q, Yuan Z Z. Model-free control of affine chaotic systems [J]. Physics Letters A, 2005, 344(2-4): 189-202.
[137] Yau H T, Chen C L. Chattering-free fuzzy sliding-mode control strategy for uncertain chaotic systems [J]. Chaos, Solitons & Fractals, 2006, 30(3): 709-718.
[138] Yan J J. Design of robust controllers for uncertain chaotic systems with nonlinear inputs [J]. Chaos, Solitons & Fractals, 2004, 19(3): 541-547.
[139] Yau H T, Yan J J. Chaos synchronization of different chaotic systems subjected to input nonlinearity [J]. Applied Matehematics and Computation, 2008, 197(2): 775-788.
[140] Chen L, Chen G R, Lee Y W. Fuzzy modeling and adaptive control of uncertain chaotic systems [J]. Information Sciences, 1999, 121(1-2): 27-37.
[141] Guan X P, Chen C. Adaptive fuzzy control for chaotic systems with H∞tracking performance [J]. Fuzzy Sets and Systems, 2003, 139(1): 81-93.
[142] Almeida R D, Alvarez J, Barajas J G. Robust synchronization of Sprott circuits using sliding mode control [J], Chaos, Solitons & fractals, 2006, 30(1): 11-18.
[143] Wu T, Chen M S. Chaos control of the modified Chua’s circuit system [J]. Physica D: Nonlinear Phenomena, 2002, 164(1-2): 53-58.
[144] R?ssler O E. An equation for continuous chaos [J]. Physics Letters A, 1976, 57(5): 397-398.
[145] Lorenz E N. Deterministic non-periodic flow [J]. Jouranl of Atmospheric, Science, 20: 130-141.
[146]张波,李忠,毛宗源等.一类永磁同步电动机混沌模型与霍夫分叉[J].中国电机工程学报, 2001, 21(9): 13-17.
[147] LüJ, Chen G. A new chaotic attractor coined [J]. International Journal of Bifurcation and Chaos,2002, 12(3): 659-661.
[148] Danca M F. On a generalized Lorenz canonical form of chaotic systems [J]. 2002, 12(8): 1789-1812.
[149] Wu X F, Chen G R, Cai J P. Chaos synchronizaiton of the master-slave generalized Lorenz systems via linear state error feedback control [J]. Physica D: Nonlinear Phenomena, 2007, 229(1): 52-80.
[150] Liu C, Liu T, Liu L. A new chaotic attractor [J], Chaos solitons & Fractals, 2004, 22(5): 1031-1038.
[151] Zhu C X, Chen Z G. Feedback control strategies for the Liu chaotic system [J]. Physics Letters A, 2008, 372(22): 4033-4036.
[152] Yassen M T. Controlling, synchronization and tracking chaotic Liu system using active backstepping design [J]. Physics Letters A, 2007, 360(4-5): 582-587.
[153] R?ssler O E. An equation for hyperchaos [J]. Physics Letters A, 1979, 71(2-3): 155-157.
[154] Yoo S J, Park J B, Choi Y H. Adaptive dynamic surface control for stabilization of parametric strict-feedback nonlinear systems with unknown time delays [J]. IEEE Trans. Automatic Control, 2007, 52(12): 2360-2365.
[155] Sanner R M, Slotine J E. Gaussian networks for direct adaptive control [J]. IEEE Trans. Neural Networks, 1992, 3(6): 837-863.
[2]朱亮.空天飞行器不确定非线性鲁棒控制[D].南京:南京航空航天大学,2006.
[3]丁青青,王树民,郭静波. HVDC非仿射非线性系统的定电流定电压控制[J].清华大学学报(自然科学版), 2004, 44(10): 1325-1328.
[4]汤洪海,李春文.基于非仿射非线性模型的AC/DC系统H∞鲁棒控制器设计[J].自动化学报, 2007, 33(7): 709-713.
[5] Mutha R K, Cluett W R, Penlidis A. Nonlinear model-based predictive control of control nonaffine systems [J]. Automatica, 1997, 33(5): 907-913.
[6] Krstic M, Kanellakopoulos I, Kokotovic P V. Nonlinear and Adaptive control design [M]. Wiley, New York, 1995.
[7]冯纯伯,费树岷.非线性控制系统分析与设计[M].第二版,北京:电子工业出版社,1997.
[8] Chiasson J. A New Approach to Dynamic Feedback Linearization Control of an Induction Motor [J]. IEEE Transations on Automatic Control, 1998, 43(3): 391-396.
[9] Hamzaoui A, Essounbouli N, Benmahammed K, et al. State observer based robust adaptive fuzzy controller for nonlinear uncertain and perturbed systems [J]. IEEE Trans. Systems, Man Cybernetics-Part B: Cybernetics, 2004, 34(2): 942-950.
[10] Park J H, Park G T, Kim S H, et al. Direct adaptive self-structuring fuzzy controller for nonaffine nonlinear system [J]. Fuzzy Sets and Systems. 2005, 153 (3), 429-445.
[11] Chen W S. Adaptive Backstepping dynamic surface control for systems with periodic disturbances using neural networks [J]. IET Control Theory and Applications, 2009, 3(10): 1383-1394.
[12] Ge S S, Wang C. Adaptive neural control of uncertain MIMO nonlinear systems [J]. IEEE Transactions on Neural Networks, 2004, 15(3): 674-692.
[13]王立新著,王迎军译.模糊系统与模糊控制[M].北京:清华大学出版社,2003.
[14]胡海岩,王在华.论迟滞与时滞[J],力学学报, 2010, 42(7): 740-746.
[15] Jiang X F, Han Q L. New stability criteria for linear systems with interval time-varying delay [J]. Automatica, 2008, 44(10): 2680-2685.
[16] Liu Y J, Wang W. Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems[J]. Information Sciences, 2007, 177 (18): 3901-3917.
[17] Leu Y G, Wang W Y, Lee T T. Observer-based direct adaptive fuzzy-neural control for nonaffine nonlinear systems [J]. IEEE Transactions on neural networks, 16(4): 853-861.
[18] Lin W. Time-varying feedback control of nonaffine nonlinear systems without drift [J]. Systems & Control Letters, 1996, 29(2): 101-110.
[19] Schiff S J, Jerger K, Duong D H, et al. Controlling chaos in the brain [J]. Nature, 1994, 370(2): 615-620.
[20] Petrov V, Gaspar V, Masere J, et al. Controlling chaos in the Belousov-Zhabotinsky reaction [J]. Nature, 1993, 361:240-243.
[21]黄润生.混沌及其应用[M].武汉:武汉大学出版社, 2003.
[22] Li C D, Liao X F, Wang K W. Chaotic lag synchronization of coupled time-delayed systems and its applications in secure communication [J]. Physica D: Nonlinear Phenomena, 2004, 194 (3-4): 187-202.
[23] Gámez-Guzmán L, Crue-Hernández C, López-Gutiérrez R M, et al. Synchronization of Chua’s circuits with multi-scroll attracors: application to communication [J]. Communications in Nonlinear Science and Numerical Simulation, 2009, 14(6): 2765-2775.
[24] Wu T Y, Chen M S. Chaos control of the modified Chua’s circuit system [J]. Physica D: Nonlinear Phenomena, 2002, 164(1-2): 53-58.
[25] Botmart T C, Niamsup P. Adaptive control and synchronization of the perturbed Chua’s system [J]. Mathematics and Computers in Simulation, 2007, 75(1-2): 37-55.
[26] Mahmoud G M, Mohamed A A, Aly S A. Strange attractors and chaos control in periodically forced complex Duffing’s oscillators [J]. Physica A: Statistical Mechanics and its Applications, 2001, 292(1-4): 193-206.
[27] Qi G Y, Chen Z Q, Yuan Z Z. Model-free control of affine chaotic systems [J]. Physics Letters A, 2005, 344(2-4): 189-202.
[28] Bagheri A, Moghaddam J J. Decoupled adaptive neuro-fuzzy (DANF) sliding mode control system for Lorenz chaotic problem [J]. Expert Systems with Applications, 2009, 36(2): 6062-6068.
[29] Park C W, Lee C H, Park M. Design of an adaptive fuzzy model based controller for chaotic dynamics in Lorenz systems with uncertainty [J]. Information Sciences, 2002, 147(1-4): 245-266.
[30] Rafikov M, Balthazar J M. On an optimal control design for R?ssler system [J]. Physics LetterA, 2004, 333(3-4): 241-245.
[31] Sun J T, Zhang Y P. Impulsive control of R?ssler system [J]. Physics Letter A, 2003, 306(5-6): 306-312.
[32] Zadeh L A. Fuzzy sets [J]. Information and Control, 1965, 8(3): 338-353.
[33] Zadeh L A. Outline of a new approach to the analysis of complex systems and decision processes [J]. IEEE Trans. Syst. Man, Cybern, 1973, 3(1): 28-44.
[34] Wang L X. Fuzzy systems are universal approximators [C]. Proceeding of IEEE International Conf. on Fuzzy Systems, San Diego, USA, 1992: 1163-1170.
[35] Kanellakopoulos I, Kokotovic P V, Morse A S. Systematic design of adaptive controllers for feedback linearizable systems [J], IEEE Trans. Automat Contr., 1991, 36(11):1241-1253.
[36] Jiang Z P, Hill D J. A robust adaptive Backstepping scheme for nonlinear systems with unmodeled dynamics [J]. IEEE Trans Automat Contr., 1999, 44(9): 1705-1711.
[37] Li J H, Lee P M. A neural network adaptive controller design for free-pitch-angle diving behavior of an autonomous underwater vehicle [J]. Robotics and Autonomous Systems, 2005, 52(2-3): 132-144.
[38] Li T S, Yang Y S, Hong B G, et al. A robust adaptive nonlinear control approach to ship straight-path tracking design [C], American control conference, Portland, 2005: 4016-4021.
[39] Marquez-Martinez L A, Moon C H. Input-output feedback linearization of time-delay systems [J]. IEEE Trans. Automatic Control, 2004, 49(5): 781-785.
[40] Ma X, Tao G. Adaptive actuator compensation control with feedback linearizaiton [J]. IEEE Trans. Automatic Control, 2000, 45(9): 1705-1710.
[41] Rugh W J, Shamma J S. Research on gain scheduling [J]. Automatica, 2000, 36(10): 1401- 1425.
[42] Tan S H, Hang C C, Chai J S. Gain scheduling: from conventional to neural-fuzzy [J]. Automatica, 1997, 33(3): 411-419.
[43] Utkin V I. Variable Structure systems with sliding modes [J]. IEEE Trans. Automatic Control, 1977, 22(2): 212-222.
[44]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): 407-418.
[45] Jiang A P, Nijmeijer H. Tracking control of mobile robots: A case study in Backstepping [J]. Automatica, 1997, 33(7): 1393-1399.
[46] Jiang Z P. A combined Backstepping and small-gain approach to adaptive output feedbackontrol [J]. Automatica, 1999, 35(6): 1131-1139.
[47] Cho Y W, Prak C W, Park M. An indirect model reference adaptive fuzzy control for SISO Takagi-Sugeno model [J]. Fuzzy Sets and Systems, 2002, 131(2), 197-215.
[48] Phan P A, Gale T J. Direct adaptive fuzzy control with a self-structuring algorithm [J]. Fuzzy Sets and Systems, 2008, 159(8): 871-899.
[49] Leu Y G, Lee T T, Wang W Y. Observer-based adaptive fuzzy-neural control for unknown nonlienar dynamical system [J]. IEEE Trans. Systems, Man Cybernetics-Part B: Cybernetics, 1999, 29(5): 583-591.
[50] Wang W Y, Leu Y G, Lee T T. Out-feedback control of nonlinear systems using direct adaptive fuzzy-neural controller [J]. Fuzzy Sets and Systems, 2003, 140(2): 341-358.
[51] Park J H, Park G T, Kim. S.H, Kim S H, et al. Output-feedback control of uncertain nonlinear systems using a self-structuring adaptive fuzzy observer [J]. Fuzzy Sets and Systems, 2005, 151(1): 21-42.
[52] Hamzaoui A, Essounbouli N, Benmahammed K, et al. State observer based robust adaptive fuzzy controller for nonlinear uncertain and perturbed systems [J]. IEEE Trans. Systems, Man Cybernetics-Part B: Cybernetics, 2004, 34(2): 942-950.
[53] Boulkroune A, Tadjine M, Saad M M’, et al. How to design a fuzzy adaptive controller based on observers for uncertain affine nonlinear systems [J]. Fuzzy Sets and Systerms, 2008, 159(8) 926-948.
[54] Yang Y S, Feng G, Ren J S. A combined Backstepping and small-gain approach to robust adaptive fuzzy control for strict-feedback nonlinear system [J]. IEEE Trans. Systems. Man, Cybernetics–Part A: System and Humans, 2004, 34(3): 406-420.
[55] Taylor D G, Kokotovic P V, Marino R, et al. Adaptive regulation of nonlinear systems with unmodeled dynamics [J]. IEEE Trans. Automatic Control, 1989, 34(4): 405-412.
[56] Pomet J B, Praly L. Adaptive nonlinear regulation: estimation from the Lyapunov equation. IEEE Trans. Automatic Control, 1992, 37(6): 729-740.
[57] Barmish B R, Leitmann G. On ultimate boundedness control of uncertain systems in the absence of matching assumptions [J]. IEEE Trans. Automatic Control, 1982, 27(1): 153-158.
[58] Corless M, Leitmann G. Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems [J]. IEEE Trans. Automatic Control, 1981, 26(5): 1139-1144.
[59] Fabri S, Kadirkamanathan V. Dynamic structure neural networks for stable adaptive control of nonlinear systems. IEEE Trans. Neural Networks, 1996, 7(5): 1151-1167.
[60] Wang L X. Stable adaptive fuzzy control of nonlinear systems. IEEE Trans. Fuzzy System, 1993, 1(2): 146-155.
[61] Kanellakopoulos I, Kokotovic P V, Morse A S. Systematic design of adaptive controller for feedback linearizable systems [J]. IEEE Trans. Automatic Control, 1991, 36(11): 1241-1253.
[62] Marino R, Tomei P. Global adaptive output-feedback control of nonlinear systems, part II: nonlinear parameterization [J]. IEEE Trans. Automatic Control, 1993, 38(1): 33-49.
[63] Wang W Y, Chan M L, Lee T T, et al. Adaptive fuzzy control for strict-feedback canonical nonlinear systems with tracking performance [J]. IEEE Trans. Systems, Man Cybernetics-Part B: Cybernetics, 2000, 30(6): 878-885.
[64] Yao B, Tomizuka M. Adaptive robust control of SISO nonlinear systems in a semi-strict feedback form [J]. Atutomatica, 1997, 33(5): 893-900.
[65] Ge S S, Wang C. Adaptive control of uncertain Chua’s circuits [J]. IEEE Trans. On Circuits Systems-I: Fundamental Theory and Applications, 2000, 47(9): 1397-1402.
[66] Chang Y C. Intelligent robust tracking control for a class of uncertain strict-feedback nonlinear systems [J]. IEEE Trans. Systems, Man Cybernetics-Part B: Cybernetics, 2000, 39(1): 142-155.
[67] Zhou S S, Feng G, Feng C B. Robust control for a class of nonlinear systems: adaptive fuzzy approach based on Backstepping [J]. Fuzzy Sets and Systems, 2005, 151(1): 1-20.
[68] Li Y H, Qiang S, Zhang X Y, et al. Robust and adaptive Backstepping control for nonlinear systems using RBF neural networks [J]. IEEE Trans. Neural Networks, 2004, 15(3): 693-701.
[69] Ge S S, Wang C. Adaptive NN control of uncertain nonlinear pure-feedback systems [J]. Automatica, 2002, 38(4): 671-682.
[70] G S S, Wang C. Direct adaptive NN control of a class of nonlinear systems [J]. IEEE Trans. Neural Networks, 2002, 13(1): 214-221.
[71] Chen W S, Jiao L C. Adaptive tracking for periodically time-varying and nonlinear parameterized systems using multilayer neural networks [J]. IEEE Trans. Neural Networks, 2010, 21(2): 345-351.
[72] Chen B, Liu X P, Liu K F, et al. Direct adaptive fuzzy control of nonlinear strict-feedback systems [J]. Automatica, 2009, 45(6): 1530-1535.
[73] Wang M, Chen B, Dai S L. Direct adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear systems [J]. Fuzzy Sets and Systems, 2007, 158(24): 2655-2670.
[74] Ho H F, Wong Y K, Rad A B. Adaptive fuzzy approach for a class of uncertain nonlinear systems in strict-feedback form [J]. ISA Transactions, 2008, 47(3): 286-299.
[75] Yang Y S, Zhou C J. Robust adaptive fuzzy tracking control for a class of perturbed strict- feedback nonlinear systems via small-gain approach [J]. Infromation Sciences, 2005, 170(2-4): 211-234.
[76] Tong S C, Li Y M, Shi P. Fuzzy adaptive Backstepping robust control for SISO nonlinear system with dynamic uncertains [J]. Infromation Sciences, 2009, 179(9): 1319-1332.
[77] Tong S C, He X L, Li Y M, et al. Adaptive fuzzy Backstepping robust control for uncertain nonlinear systems based on small-gain approach [J]. Fuzzy Sets and Systems, 2010, 161(6): 771-796.
[78] Yang Y S, Zhou C J. Adaptive fuzzy H∞stabilization for strict-feedback canonical nonlinear systems via Backstepping and small-gain approach [J]. IEEE Trans. Fuzzy Systems, 2005, 13(1): 104-114.
[79] Zhang T P, Ge S S. Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form [J]. Automatica, 2008, 44(7): 1895-1903.
[80] Wang D, Huang J. Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form [J]. IEEE Trans. Neural Networks, 2005, 16(1): 195-202.
[81] Ge S S, Wang J. Robust adaptive neural control for a class of perturbed strict-feedback nonlinear systems [J]. IEEE Trans. Neural Networks, 2002, 13(6): 1409-1419.
[82] Li J, Chen W S, Li J M, et al. Adaptive NN output-feedback stabilization for a class of stochastic nonlinear strict-feedback systems [J]. ISA Transactions, 2009, 48(4): 468-475.
[83] Tong S C, Li Y M. Observer-based fuzzy adaptive control for strict-feedback nonlinear systems [J]. Fuzzy Sets and Systems, 2009, 160(12): 1749-1764.
[84] Chen B, Liu X P, Tong S C. Adaptive fuzzy output tracking control of MIMO nonlinear uncertain systems [J]. IEEE Trans. Neural Networks, 2007, 15(2): 287-300.
[85] Liu Y J, Wang W, Tong S C, et al. Robust Adaptive tracking control for nonlinear systems based on bounds of fuzzy approximation parameters [J]. IEEE Trans. Systems. Man, Cybernetics–Part A: System and Humans, 2010, 40(1): 170-184.
[86] Li T S, Tong S C, Feng G. A novel robust adaptive-fuzzy-tracking control for a class of nonlinear multi-input/multi-output systems [J]. IEEE Trans. Fuzzy Systems, 2010, 18(1): 150-160.
[87] Chen B, Liu X P. Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by Backstepping and application to chemical processes [J]. IEEE Trans. Fuzzy Systems, 2005,13(6): 832-847.
[88] Chen B, Tong S C, Liu X P. Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by Backstepping approach [J]. Fuzzy Sets and Systems, 2007, 158(10): 1097-1125.
[89] Zou A M, Hou Z G, Tan M. Adaptive control of a class of nonlinear pure-feedback systems using fuzzy Backstepping approach [J]. IEEE Trans. Fuzzy Systems, 2008, 16(4): 886-896.
[90] Yoo S J, Park J B, Choi Y H. Adaptive neural control for a class of strict-feedback nonlinear systems with state time delays [J]. IEEE Trans. Neural Networks, 2009, 20(7): 1209-1215.
[91] Ge S S, Hong F, Lee T H. Adaptive neural network control of nonlinear systems with unknown time delays [J]. IEEE Trans. Automatic Control, 2003, 48(11): 2004-2010.
[92] Ge S S, Tee K P. Approximation-based control of nonlinear MIMO time-delay systems [J]. Automatica, 2007, 43(1): 31-43.
[93] Wang M, Chen B, Liu X P, et al. Adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear time-delay systems [J]. Fuzzy Sets and Systems, 2008, 159(8): 949-967.
[94] Wang M, Chen B, Shi P. Adaptive neural control for a class of perturbed strict-feedback nonlinear time-delay systems [J]. IEEE Trans. Systems, Man Cybernetics-Part B: Cybernetics, 2008, 38(3): 721-730.
[95] Chen B, Liu X P, Liu K F, et al. Fuzzy-approximation-based adaptive control of strict-feedback nonlinear systems with time delays [J]. IEEE Trans. Fuzzy Systems, 2010, 18(5): 883-892.
[96] Chen B, Liu X P, Liu K F, et al. Novel adaptive neural control design for nonlinear MIMO time-delay systems [J]. Automatica, 2009, 45(6): 1554-1560.
[97] Hua C C, Feng G, Guan X P. Robust controller design of a class of nonlinear time delay systems via backstepping method. Automatic, 2008, 44(2): 567-573.
[98] Chen B, Liu X P, Liu K F, et al. Direct adaptive fuzzy control for nonlinear systems with time-varying delays [J]. Informaiton Sciences, 2010, 180(5): 776-792.
[99]沈启坤,张天平,钱厚斌.一类非仿射非线性系统的自适应模糊控制[J].电机与控制学报,2006, 10(6): 592-596.
[100]胡慧,刘国荣,郭鹏等.基于观测器的一类非仿射非线性系统的自适应神经网络H∞跟踪控制[J],信息与控制, 2009, 38(4): 468-472.
[101] Hovakimyan N, Nardi F, Calise A J. A novel error observer-based adaptive output feedback approach for control of uncertain systems [J]. IEEE Trans. Automatic Control, 2002, 47(8): 1310-1314.
[102] Yang B J, Calise A J. Adaptive control of a class of nonaffine systems using neural networks [J]. IEEE Trans. Neural Networks, 2007, 18(4): 1149-1159.
[103] Teo J, How J P, Lavretsky E. Proportional-integral controllers for minimum-phase nonaffine -in-control systems [J]. IEEE Trans. Automatic control, 2010, 55(6): 1477-1483.
[104] Zhao T. RBFN-based decentralized adaptive control of a class of large-scale non-affine nonlinear sytems [J]. Neural Comput & Applic., 2008, 17(4): 357-364.
[105] Boulkroune A, Tadjine M, M’Saad M, et al. Adaptive fuzzy control for non-affine systems with zero dynamics [J]. International Journal of Systems Science, 2009, 40(4): 367-382.
[106] Tee K P, Ge S S, Tay E H. Adaptive neural network control for helicopters in vertical flight [J]. IEEE Trans. Control Systems Technology, 2008, 16(4): 753-762.
[107] Du H B, Chen X C. NN-based output feedback adaptive variable structure control for a class of non-affine nonlinear systems: A nonseparation principle design [J]. Neurocomputing, 2009, 72(2-9): 2009-2016.
[108] Labiod S, Guerra T M. Adaptive fuzzy control of a class of SISO nonaffine nonlinear systems [J]. Fuzzy Sets and Systems, 2007, 158(10): 1126-1137.
[109] Park J H, Park G T, et al. Direct adaptive self-structuring fuzzy controller for nonaffine nonlinear system [J]. Fuzzy Sets and Systems, 2005, 153 (3): 429-445.
[110] Park J H, Kim S H. Direct adaptive output-feedback fuzzy controller for a nonaffine nonlinear system [J]. IEE Proc.-Control Theory Appl., 2004, 151(1): 65-72.
[111] Ren B B, Ge S S, Su C Y, et al. Adaptive neural control for a class of uncertain nonlinear systems in pure-feedback form with hysteresis input [J]. IEEE Trans. Systems, Man Cybernetics-Part B: Cybernetics, 2009, 39(2): 431-443.
[112]杜红彬,邵惠鹤.一类非线性系统的自适应模糊神经网络控制[J].控制与决策, 2005, 20(4): 454-458.
[113]杜红彬,李绍军.一类纯反馈非仿射非线性系统的自适应神经网络变结构控制[J].系统工程与电子技术, 2008, 30(4): 723-726.
[114] Zou A M, Hou Z G, Tan M. Adaptive control of a class of nonlinear pure-feedback systems using fuzzy backstepping approach [J]. IEEE Trans. Fuzzy Systems, 2008, 16(4): 886-897.
[115]刘艳军,王伟.一类多变量非线性系统的自适应模糊控制[J].自动化学报, 2007, 33(11): 1163-1169.
[116] Liu Y J, Wang W. Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems [J]. Information Sciences, 2007, 177(18): 3901-3917.
[117] Liu Y J, Tong S C, Wang W. Adaptive fuzzy output tracking control for a class of uncertain nonlinear systems [J]. Fuzzy Sets and Systems, 2009, 160(19): 2727-2754.
[118] Wang M, Ge S S, Hong K S. Approximation-based adaptive tracking control of pure-feedback nonlinear systems with multiple unknown time-varying delays [J]. IEEE Trans. Neural Networks, 2010, 21(11): 1804-1816.
[119] Ren B B, Ge S S, Lee T H, et al. Adaptive neural control of SISO non-affine nonlinear time-delay systems with unknown hysteresis input [C], American control conference, Washington, USA, 2008: 4203-4208.
[120] Lin S C, Chen Y Y. Design of self-learning fuzzy sliding mode controllers based on genetic algorithms [J]. Fuzzy Sets and Systems, 1997, 86(2): 139-153.
[121] Alfaro-Cid E, McGookin E W, Murray-Smith D J. A comparative study of genetic operators for controller parameter optimization [J]. Control Engineering Pracctice, 2009, 17(1): 185-197.
[122] Cazarez-Castro N R, Aguilar L T, Castillo O. Fuzzy logic control with genetic membership function parameters optimization for the output regulation of a servomechanism with nonlinear backlash [J]. Expert Systems with Applications, 2010, 37(6): 4368-4378.
[123] Li R H, Zhang Y. Fuzzy logic controller based on genetic algorithms [J]. Fuzzy Sets and Systems, 1996, 83(1): 1-10.
[124] Onnen C, Babuska R, Kaymak U, et al. Genetic algorithms for optimization in predictive control [J]. 1997, 5(10): 1363-1372.
[125] Fleming P J, Purshouse R C. Evolutionary algorithms in control systems engineering: a survey [J]. Control Engineering Practices, 2002, 10(11): 1223-1241.
[126] Giordano V, Naso D, Turchiano B. Combining genetic algorithms and Lyapunov-based adaptive for online design of fuzzy controllers [J]. IEEE Trans. Systems, Man Cybernetics-Part B: Cybernetics, 2006, 36(5): 1118-1126.
[127] Ioannou P A, Sun J. Robust adaptive control [M]. Prentice-Hall, Englewood Cliffs, NJ, 1996.
[128] Polycarpou M M, Ioannou P A. A robust adaptive nonlinear control design [J]. Automatica, 1996, 32(3): 423-427.
[129] Ablay G. Sliding mode control of uncertain unified chaotic systems [J]. Nonlinear Analysis: Hybrid Systems, 2009, 3(4): 531-535.
[130] Zhou J, Er M J. Adaptive output control of a class of uncertain chaotic systems [J]. Systems & Control Letters, 2007, 56(6): 452-460.
[131] Lu Z, Shieh L S, Chen G R, et al. Adaptive feedback linearization control of chaotic systems viarecurrent high-order neural networks [J]. Information Sciences, 2006, 176(16): 2337-2354.
[132] Noroozi N, Roopaei M, Karimaghaee P, et al. Simple adaptive variable structure control for unknown chaotic systems [J]. Communications in Nonlinear Science and Nnmerical Simulaiton, 2010, 15(3): 707-727.
[133] Poursamad A, Davaie-Markazi A H. Robust adaptive fuzzy control of unknown chaotic systems [J]. Applied Soft Computing, 2009, 9(3): 970-976.
[134] Lin D, Wang X Y, Nian F Z, et al. Dynamic fuzzy neural networks modeling and adaptive backstepping tracking control of uncertain chaotic systems [J]. Neurocomputing, 2010, 73(16- 18): 2873-2881.
[135] Ting C S. An observer-based approach to controlling time-dealy chaotic systems via Takagi- sugeno fuzzy model [J]. Information Sciences, 2007, 177(20): 4314-4328.
[136] Qi G Y, Chen Z Q, Yuan Z Z. Model-free control of affine chaotic systems [J]. Physics Letters A, 2005, 344(2-4): 189-202.
[137] Yau H T, Chen C L. Chattering-free fuzzy sliding-mode control strategy for uncertain chaotic systems [J]. Chaos, Solitons & Fractals, 2006, 30(3): 709-718.
[138] Yan J J. Design of robust controllers for uncertain chaotic systems with nonlinear inputs [J]. Chaos, Solitons & Fractals, 2004, 19(3): 541-547.
[139] Yau H T, Yan J J. Chaos synchronization of different chaotic systems subjected to input nonlinearity [J]. Applied Matehematics and Computation, 2008, 197(2): 775-788.
[140] Chen L, Chen G R, Lee Y W. Fuzzy modeling and adaptive control of uncertain chaotic systems [J]. Information Sciences, 1999, 121(1-2): 27-37.
[141] Guan X P, Chen C. Adaptive fuzzy control for chaotic systems with H∞tracking performance [J]. Fuzzy Sets and Systems, 2003, 139(1): 81-93.
[142] Almeida R D, Alvarez J, Barajas J G. Robust synchronization of Sprott circuits using sliding mode control [J], Chaos, Solitons & fractals, 2006, 30(1): 11-18.
[143] Wu T, Chen M S. Chaos control of the modified Chua’s circuit system [J]. Physica D: Nonlinear Phenomena, 2002, 164(1-2): 53-58.
[144] R?ssler O E. An equation for continuous chaos [J]. Physics Letters A, 1976, 57(5): 397-398.
[145] Lorenz E N. Deterministic non-periodic flow [J]. Jouranl of Atmospheric, Science, 20: 130-141.
[146]张波,李忠,毛宗源等.一类永磁同步电动机混沌模型与霍夫分叉[J].中国电机工程学报, 2001, 21(9): 13-17.
[147] LüJ, Chen G. A new chaotic attractor coined [J]. International Journal of Bifurcation and Chaos,2002, 12(3): 659-661.
[148] Danca M F. On a generalized Lorenz canonical form of chaotic systems [J]. 2002, 12(8): 1789-1812.
[149] Wu X F, Chen G R, Cai J P. Chaos synchronizaiton of the master-slave generalized Lorenz systems via linear state error feedback control [J]. Physica D: Nonlinear Phenomena, 2007, 229(1): 52-80.
[150] Liu C, Liu T, Liu L. A new chaotic attractor [J], Chaos solitons & Fractals, 2004, 22(5): 1031-1038.
[151] Zhu C X, Chen Z G. Feedback control strategies for the Liu chaotic system [J]. Physics Letters A, 2008, 372(22): 4033-4036.
[152] Yassen M T. Controlling, synchronization and tracking chaotic Liu system using active backstepping design [J]. Physics Letters A, 2007, 360(4-5): 582-587.
[153] R?ssler O E. An equation for hyperchaos [J]. Physics Letters A, 1979, 71(2-3): 155-157.
[154] Yoo S J, Park J B, Choi Y H. Adaptive dynamic surface control for stabilization of parametric strict-feedback nonlinear systems with unknown time delays [J]. IEEE Trans. Automatic Control, 2007, 52(12): 2360-2365.
[155] Sanner R M, Slotine J E. Gaussian networks for direct adaptive control [J]. IEEE Trans. Neural Networks, 1992, 3(6): 837-863.