几类非线性系统的自适应Backstepping模糊控制研究
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摘要
近些年来,由于被控对象和控制目标越来越复杂,逐渐建立起来很多新的控制理论.对于复杂非线性系统的控制问题现在比较有效的控制方法仍然是模糊控制方法.另外,由于该控制理论的不断发展,人们越来越关注其在实际生活生产中的应用.在现有的模糊控制理论中,模糊逻辑系统(FLS)控制方法越来越多的受到诸多学者的关注.而对于该类控制方法而言其主要优点在于可以运用专家学者的先验知识来研究非线性系统的稳定性以及控制器设计问题.但是运用该方法的劣势在于由于模糊逻辑系统本身的特点造成了没有系统的稳定性理论分析方法,这也是使用模糊逻辑系统控制方法的挑战性所在.另一方面,在控制器设计过程中随着模糊规则数的增加使得在线调节的参数也不断的增大,所以对于实际的工业系统而言在控制器的设计过程中减小调节参数个数也是极其有必要的.另外,在实际系统中时间延时是造成系统不稳定的主要因素之一,在本文中针对具有离散或者分布时变时延的非线性系统,设计出有效的模糊自适应控制器.同时为了减小系统的运算负担所提控制器含有较少自适应参数.具体来说我们取得了以下研究成果：
1.基于合理的假设,采用合适的Lyapunov-Krasovskii泛函处理系统中的未知时变时滞项,同时运用FLS逼近系统中的未知非线性连续函数,另外采用Nussbaum类型的函数探测系统的控制方向,最后基于backstepping技术分别对具有离散时间延时和未知控制方向的非线性系统以及具有分布时间延时和未知控制方向的非线性系统设计状态反馈模糊自适应跟踪控制器.同时,控制器中含有较少的自适应参数,从而使得控制器的运用更加方便有效.
2.基于合理的假设和线性状态观测器,运用适当的Lyapunov-Krasovskii泛函, Nuss-baum类型的函数,最小学习参数(MLP)算法, FLS以及backstepping技术分别对具有未知控制方向的时变时延系统和具有未知控制方向以及输入时延的非线性系统设计出有效的模糊自适应输出反馈控制器.值得一提的是,在控制器设计之前通过一个线性变换将分散在系统中的未知控制系数整合到一个系数中去,从而变为对比较常见的只有一个未知控制方向的系统的输出反馈控制问题的研究,且值得注意的是控制器中含有较少待估参数.
3.运用恰当的Lyapunov-Krasovskii泛函,动态面控制(DSC)技术, MLP算法, FLS以及backstepping技术分别针对具有未知死区的时变时延非线性系统和具有输入时延的MIMO非线性系统设计出含有较少待估参数的模糊自适应控制器.值得指出的是DSC技术的选用有效的避免了采用backstepping技术产生的“参数爆炸”问题,从而有效地简化了控制器设计过程.另外控制器中含有非常少的自适应参数(1个或2个)极大地减少了在线运算量.
4.现有研究随机非线性系统跟踪控制器结果大多是利用四次Lyapunov函数或者是结合传统的二次Lyapunov函数和风险灵敏度准则处理问题.而在本文中作者引进双曲正切函数处理Ito微分产生的高阶Hessian项,再结合传统的二次Lyapunov函数、backstepping技术以及FLS为具有时变时滞的随机非线性系统设计出有效的模糊自适应跟踪控制器.
In recent years, many new control theories have been gradually established because ofthe controlled plants and the control objectives becoming more and more complex. For thecontrol problem of the complex nonlinear systems, the much more effective control methodis the fuzzy control technology. Moreover, the applications of the fuzzy control theory in theactual production and daily life has been concerned with its development. In the existing fuzzycontrol theory, the fuzzy logic systems(FLS) control method receives more and more attentionfrom the scholars. The main advantage of the method is that it can combine some experienceand knowledge from designers or experts to investigate the stability and the controller designproblem of the nonlinear systems. However, the main disadvantage of the method is that due tothe characteristic of the FLS such that there is no systematic stability theory analysis method,and this also is the challenging of the use of the FLS control method. On the other hand, duringthe controller design process, the number of the adjusted parameters depends on the number ofthe fuzzy rule bases. With an increase of fuzzy rules, the number of parameters to be estimatedwill increase significantly, therefore, for the actual industrial systems, during the controllerdesign process, it is extremely necessary to design the controller containing much less adjustedparameters. In addition, in the practical systems, the time delay is one of the main factorswhich make the system unstable. In this dissertation, the effective adaptive fuzzy controllersare proposed for the nonlinear systems with discrete or distributed time-varying delays. And inorder to reduce the online computation burden of the systems, the proposed controllers containmuch less adjusted parameters. Specifically, we obtain the following research results.
1. Based on the reasonable assumptions, by utilizing the appropriate Lyapunov-Krasovskiifunctional, the FLS and the Nussbaum-type functions to deal with the unknown time-varyingdelay terms, approximate the unknown nonlinear continuous functions and detect the controldirections of the systems, respectively, finally, for the nonlinear systems with discrete timedelays and unknown control directions and the nonlinear systems with distributed time delaysand unknown control directions, the adaptive fuzzy tracking controllers are designed by usingthe backstepping technique. Moreover, the proposed controllers contain much less adjustedparameters such that the use of the controllers are much more convenient and effective.
2. Based on the reasonable assumptions and the linear state observer, for the time-varyingdelay nonlinear systems with unknown control directions and the nonlinear systems with inputdelay, the output feedback adaptive fuzzy controllers are proposed by combining the properLyapunov-Krasovskii functional, the Nussbaum-type functions, the minimal learning parame-ters (MLP) algorithm, the FLS and the backstepping technique. It is should be pointed out thatbefore the controllers are designed, we introduce a linear state transformation, through which the unknown control coefficients distributed in the system can be lumped together, then, theproblem is become that how to design the output feedback controllers for the relatively com-mon systems with only one unknown direction, and it is worth noting that the controllers containmuch less adjusted parameters.
3. For the nonlinear time-varying delay systems with unknown dead zone and the MIMOnonlinear system with input delays, the adaptive fuzzy controllers which contain much lessadjusted parameters are constructed by combining the proper Lyapunov-Krasovskii functional,the dynamic surface control (DSC) technique, the MLP algorithm, the FLS and the backsteppingtechnique. It is should be pointed out that the use of the DSC technique effectively overcomethe“explosion of complexity” cased by the use of the backstepping technique, therefore, thecontroller design process is simplified effectively. Moreover, the controllers contain very fewadaptive parameters (one or two) such that the online computation burden is reduced greatly.
4. Most of the existing results investigating the tracking control problem of the stochasticnonlinear systems are obtained by using the quartic Lyapunov functions or by combining theclassical quadratic functions with the risk-sensitive cost criterion. However, in this dissertation,the hyperbolic tangent functions are introduced to deal with the Hessian terms which comefrom the Ito differential, and then, by applying the classical quadratic functions, the backstep-ping technique and the FLS, the effective fuzzy adaptive tracking controller is designed for thestochastic nonlinear time-varying delay system.
1.基于合理的假设,采用合适的Lyapunov-Krasovskii泛函处理系统中的未知时变时滞项,同时运用FLS逼近系统中的未知非线性连续函数,另外采用Nussbaum类型的函数探测系统的控制方向,最后基于backstepping技术分别对具有离散时间延时和未知控制方向的非线性系统以及具有分布时间延时和未知控制方向的非线性系统设计状态反馈模糊自适应跟踪控制器.同时,控制器中含有较少的自适应参数,从而使得控制器的运用更加方便有效.
2.基于合理的假设和线性状态观测器,运用适当的Lyapunov-Krasovskii泛函, Nuss-baum类型的函数,最小学习参数(MLP)算法, FLS以及backstepping技术分别对具有未知控制方向的时变时延系统和具有未知控制方向以及输入时延的非线性系统设计出有效的模糊自适应输出反馈控制器.值得一提的是,在控制器设计之前通过一个线性变换将分散在系统中的未知控制系数整合到一个系数中去,从而变为对比较常见的只有一个未知控制方向的系统的输出反馈控制问题的研究,且值得注意的是控制器中含有较少待估参数.
3.运用恰当的Lyapunov-Krasovskii泛函,动态面控制(DSC)技术, MLP算法, FLS以及backstepping技术分别针对具有未知死区的时变时延非线性系统和具有输入时延的MIMO非线性系统设计出含有较少待估参数的模糊自适应控制器.值得指出的是DSC技术的选用有效的避免了采用backstepping技术产生的“参数爆炸”问题,从而有效地简化了控制器设计过程.另外控制器中含有非常少的自适应参数(1个或2个)极大地减少了在线运算量.
4.现有研究随机非线性系统跟踪控制器结果大多是利用四次Lyapunov函数或者是结合传统的二次Lyapunov函数和风险灵敏度准则处理问题.而在本文中作者引进双曲正切函数处理Ito微分产生的高阶Hessian项,再结合传统的二次Lyapunov函数、backstepping技术以及FLS为具有时变时滞的随机非线性系统设计出有效的模糊自适应跟踪控制器.
In recent years, many new control theories have been gradually established because ofthe controlled plants and the control objectives becoming more and more complex. For thecontrol problem of the complex nonlinear systems, the much more effective control methodis the fuzzy control technology. Moreover, the applications of the fuzzy control theory in theactual production and daily life has been concerned with its development. In the existing fuzzycontrol theory, the fuzzy logic systems(FLS) control method receives more and more attentionfrom the scholars. The main advantage of the method is that it can combine some experienceand knowledge from designers or experts to investigate the stability and the controller designproblem of the nonlinear systems. However, the main disadvantage of the method is that due tothe characteristic of the FLS such that there is no systematic stability theory analysis method,and this also is the challenging of the use of the FLS control method. On the other hand, duringthe controller design process, the number of the adjusted parameters depends on the number ofthe fuzzy rule bases. With an increase of fuzzy rules, the number of parameters to be estimatedwill increase significantly, therefore, for the actual industrial systems, during the controllerdesign process, it is extremely necessary to design the controller containing much less adjustedparameters. In addition, in the practical systems, the time delay is one of the main factorswhich make the system unstable. In this dissertation, the effective adaptive fuzzy controllersare proposed for the nonlinear systems with discrete or distributed time-varying delays. And inorder to reduce the online computation burden of the systems, the proposed controllers containmuch less adjusted parameters. Specifically, we obtain the following research results.
1. Based on the reasonable assumptions, by utilizing the appropriate Lyapunov-Krasovskiifunctional, the FLS and the Nussbaum-type functions to deal with the unknown time-varyingdelay terms, approximate the unknown nonlinear continuous functions and detect the controldirections of the systems, respectively, finally, for the nonlinear systems with discrete timedelays and unknown control directions and the nonlinear systems with distributed time delaysand unknown control directions, the adaptive fuzzy tracking controllers are designed by usingthe backstepping technique. Moreover, the proposed controllers contain much less adjustedparameters such that the use of the controllers are much more convenient and effective.
2. Based on the reasonable assumptions and the linear state observer, for the time-varyingdelay nonlinear systems with unknown control directions and the nonlinear systems with inputdelay, the output feedback adaptive fuzzy controllers are proposed by combining the properLyapunov-Krasovskii functional, the Nussbaum-type functions, the minimal learning parame-ters (MLP) algorithm, the FLS and the backstepping technique. It is should be pointed out thatbefore the controllers are designed, we introduce a linear state transformation, through which the unknown control coefficients distributed in the system can be lumped together, then, theproblem is become that how to design the output feedback controllers for the relatively com-mon systems with only one unknown direction, and it is worth noting that the controllers containmuch less adjusted parameters.
3. For the nonlinear time-varying delay systems with unknown dead zone and the MIMOnonlinear system with input delays, the adaptive fuzzy controllers which contain much lessadjusted parameters are constructed by combining the proper Lyapunov-Krasovskii functional,the dynamic surface control (DSC) technique, the MLP algorithm, the FLS and the backsteppingtechnique. It is should be pointed out that the use of the DSC technique effectively overcomethe“explosion of complexity” cased by the use of the backstepping technique, therefore, thecontroller design process is simplified effectively. Moreover, the controllers contain very fewadaptive parameters (one or two) such that the online computation burden is reduced greatly.
4. Most of the existing results investigating the tracking control problem of the stochasticnonlinear systems are obtained by using the quartic Lyapunov functions or by combining theclassical quadratic functions with the risk-sensitive cost criterion. However, in this dissertation,the hyperbolic tangent functions are introduced to deal with the Hessian terms which comefrom the Ito differential, and then, by applying the classical quadratic functions, the backstep-ping technique and the FLS, the effective fuzzy adaptive tracking controller is designed for thestochastic nonlinear time-varying delay system.
引文
[1] Zadeh L A. Fuzzy sets. Information and Control,1965,8(3):338-353.
[2] Zadeh L A. Outline of a new approach to the analysis of complex systems and decisionprocesses[J]. IEEE Transactions on Systems, Man, Cybernetics,1973,3(1):28-44.
[3] Mamdani E H. Applications of fuzzy algorithms for simple dynamic plant. Proc. IEEControl and Science,1974,121(12):1585-1588.
[4] Procyk T J, Mamdani E H. A linguistic self-organizing process controller. Automatica,1979,15(1):15-30.
[5]李江荣.模糊系统的广义H2控制. PhD thesis,西安,西安电子科技大学,2012.
[6] Takagi T, Sugeno M. Fuzzy identification of systems and its applications to modeling andcontrol. IEEE Transactions on Systems, Man, Cybern. B: Cybernetics,1985,15(1):116-132.
[7]王立新.自适应模糊系统与控制–设计与稳定性分析.北京:国防工业出版社,1995.
[8] Wang L X. Adaptive fuzzy systems and control:design and stability analysis. Prentice-Hall, EnglewoodCliffs, NJ,1994.
[9] Kokotivic P V, Arcak M. Constructive nonlinear control: A historical perspective. Auto-matica,2007,37(3):637-662.
[10] Byrnes C I, Isidori A. New results and examples in nonlinear feedback stabilization.Systems and Control Letters,1989,12(5):437-442.
[11] Kokotivic P V, Sussmann H J. Posivite real condition for global stabilization of nonlinearsystems. Systems and Control Letters,1989,12(2):125-133.
[12] Saberi A, Kokotivic P V, Sussmann H J. Global stabilization of partially linear compositesystems. SIAM Journal of Control and Optimization,1990,28(6):1491-1503.
[13]胡跃明.非线性控制系统理论与应用.北京:国防工业出版社,2002.
[14]宫琪,田玉平.非线性交叉严格反馈系统的一种构造性设计方法.自动化学报,2000,26(4):447-453.
[15] Krstic′M, Kanellakopoulos I, Kokotovic P V. Nonlinear and adaptive control design.New York:Wiley,1995.
[16] Kanellakopoulos I, Kokotovic P V, Morse A S. Systematic design of adaptive con-trollers for feedback linearizable systems. IEEE Transactions on Automatic Control,1991,36(11):1241-1253.
[17] Marino R, Tomei P. Global adaptive output-feedback control of nonlinear systems, I:Linear parameterization. IEEE Transactions on Automatic Control,1993,38(1):17-32.
[18] Marino R, Tomei P. Robust stabilization of feedback linearizable time-varying uncertainnonlinear systems. Automatica,1993,29(1):181-189.
[19] Yao B, Tomizuka M. Adaptive robust control of SISO nonlinear systems in a semi-strictfeedback form. Automatica,1997,33(5):893-900.
[20]陈为胜.非线性系统智能Backstepping控制与分析. PhD thesis,西安,西安电子科技大学,2007.
[21] Krstic′M, Deng H. Stabilization of Nonlinear Uncertain Systems, London, U.K.:Springer-Verlag,1998.
[22] Boulkroune A, Tadjine M, Saad M, et al. How to design a fuzzy adaptive controllerbased on observers for uncertain affine nonlinear systems. Fuzzy Sets and Systems,2008,159(8)926–948.
[23] Golea N, Golea A, Benmahammed K. Stable indirect fuzzy adaptive control. Fuzzy Setsand Systems,2003,137(3):353–366.
[24] Golea N, Golea A, Barra K. Observer-based adaptive control of robot manipulators: fuzzysystems approach. Applied Soft Computing,2008,8(1):778–787.
[25] Tong S C, Chai T Y. Fuzzy adaptive control for a class of nonlinear systems. Fuzzy Setsand Systems,1999,101(1):31–39.
[26] Wang W Y, Chan M L, Lee T T, et al. Adaptive fuzzy control for strict-feedback canon-ical nonlinear systems with H∞tracking performance. IEEE Transactions on Systems,Man,and Cybernetics―PartB,2000,30(6):878–885.
[27] Chang Y C. Robust tracking control for nonlinear MIMO systems via fuzzy approaches.Automatica,2000,36(10):1535–1545.
[28] Chang Y C. Adaptive fuzzy-based tracking control for nonlinear SISO systems via VSSand H∞approaches. IEEE Transactions on Fuzzy Systems,2001,9(2):278–292.
[29] Chen B S, Lee C H, Chang Y C. H∞tracking design of uncertain nonlinear SISO systems:adaptive fuzzy approach. IEEE Transactions on Fuzzy Systems,1996,4(1):32–43.
[30] Spooner J T, Passino K V. Stable adaptive control using fuzzy systems and neural net-works. IEEE Transaction on Fuzzy Systems,1996,4(3):339–359.
[31] Su C Y, Stepanenko Y. Adaptive control of a class of nonlinear systems with fuzzy logic.IEEE Transactions on Fuzzy Systems,1994,2(4):285–294.
[32] Wang L X. Stable adaptive fuzzy control of nonlinear systems. IEEE Transactions onFuzzy Systems,1993,1(2):146–155.
[33] Zou A M, Kumar K D. Adaptive fuzzy fault-tolerant attitude control of spacecraft. Con-trol Engineering Practice,2011,19(1):10-212.
[34] Jagannnathan S, Lewis F L. Robust backstepping control of a class of nonlinear systemsusing fuzzy logic. Information Sciences,2000,123(3):223–240.
[35] Tong S C, Li Y, Shi P. Fuzzy adaptive backstepping robust control for SISO nonlinearsystems with dynamic uncertainties. Information Sciences,2009,179(9):1319–1332.
[36] Wang M, Chen B. Direct adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear systems. Fuzzy Sets and Systems,2007,158(24):2655–2670.
[37] Wang M, Chen B, Shi P. Adaptive neural control for a class of perturbed strict-feedbacknonlinear time-delay systems. IEEE Transactions on Systems, Man, and Cybernet-ics―PartB,2008,38(3):721–730.
[38] Tong S C, Li Y M. Observer-based fuzzy adaptive control for strict-feedback nonlinearsystems. Fuzzy Sets and Systems,2009,160(12):1749–1764
[39] Tong S C, Li Y M. Observer-based fuzzy adaptive robust control of nonlinear systemswith time delays and unmodeled dynamics. Neurocomputing,2010,74(1):369–378
[40] Zhou S S, Feng G, Feng C B. Robust control for a class of uncertain nonlinear sys-tems:adaptive fuzzy approach based on backstepping, Fuzzy Sets and Systems.2005,151(1):1-20.
[41] Li C Y, Tong S C, Wang W. Fuzzy adaptive high-gain-based observer backstepping con-trol for SISO nonlinear systems. Information Sciences,2011,181(11):2405–2421.
[42] Chen W S, Jiao L C, Li R H, et al. Adaptive Backstepping Fuzzy Control for Nonlin-early Parameterized Systems With Periodic Disturbances. IEEE Transactions on FuzzySystems,2010,18(4):674-685.
[43] Yang Y S. Direct robust adaptive fuzzy control(DRAFC) for uncertain nonlinear systemsusing small-gain theorem. Fuzzy Sets and Systems,2005,151(1):79–97.
[44] Yang Y S, Zhou C J. Adaptive fuzzy H∞stabilization for strict-feedback canonical non-linear systems via backstepping and small-gain approach. IEEE Transactions on FuzzySystems,2005,13(1):104-114.
[45] Chen B, Liu X P, Shi P. Comment on“adaptive fuzzy H∞stabilization for strict-feedback canonical nonlinear systems via backstepping and small-gain approach”. IEEETransactions on Fuzzy Systems,2009,17(3):732–733.
[46] Tong S C, He X L, Li Y M, et al. Adaptive fuzzy backstepping robust control for un-certain nonlinear systems based on small-gainapproach. Fuzzy Sets and Systems2010,161(6):771-796.
[47] Tong S C, He X L, Li Y M. Direct adaptive fuzzy backstepping robust control for singleinput and single output uncertain nonlinear systems using small-gain approach. Informa-tion Sciences,2010,180(9):1738–1758.
[48] Chen B, Liu X P, Tong S C. Fuzzy approximate disturbance decoupling of MIMO nonlin-ear systems by backstepping and application to chemical processes. IEEE Transactionson Fuzzy Systems,2005,13(6):832–847.
[49] Chen B, Liu X P, Tong S C. Fuzzy approximate disturbance decoupling of MIMO non-linear systems by backstepping approach. Fuzzy Sets and Systems,2007,158(10):1097-1125.
[50] Tong S C, Li C Y, Li Y M. Fuzzy adaptive observer backstepping control for MIMOnonlinear systems. Fuzzy Sets and Systems,2009,160(19):2755-2775.
[51] Yousef H, Hamdy M, El-Madbouly E, et al. Adaptive fuzzy decentralized control forinterconnected MIMO nonlinear subsystems. Automatica,2009,45(2):456-462.
[52] Liu Y J, Tong S C, Wang W. Adaptive fuzzy output tracking control for a class of uncer-tain nonlinear systems. Fuzzy Sets and Systems,2009,160(19):2727–2754.
[53] Niculescu S L. Delay Effects on Stability: A Robust Control Approach. Springer, London,2001.
[54] Boukas E K, Al-Muthairi N F. Delay-dependent stabilization of singular linear systemswith delays. International Journal of Innovative Computing, Information and Control,2006,2(2):283–291.
[55] Chen B, Lam J, Xu S. Memory state feedback guaranteed cost control for neutral delaysystems. International Journal of Innovative Computing, Information and Control,2006,2(2):293–303.
[56] Wang M, Chen B, Liu X P, et al. Adaptive fuzzy tracking control for a class of perturbedstrict-feedback nonlinear time-delay systems. Fuzzy Sets and Systems,2008,159(8):949-967.
[57] Wang M, Chen B, Liu K F, et al. Adaptive fuzzy tracking control of nonlinear time-delay systems with unknown virtual control coefficients. Information Sciences,2008,178(22):4326–4340.
[58] Wang M, Chen B, Tong S C. Adaptive fuzzy tracking control for strict-feedback nonlin-ear systems with unknown time delays. International Journal of Innovative Computing,Information and Control,2008,4(4):829-838.
[59] Chen B, Liu X P, Liu K F, et al. Direct adaptive fuzzy control for nonlinear systems withtime-varying delays. Information Sciences,2010,180(5):776-792.
[60] Hua C C, Wang Q G, Guan X P. Adaptive fuzzy output-feedback controller design fornonlinear time-delay systems with unknown control direction. IEEE Transactions onSystems Man Cybernet-Part B,2009,39(2):363-374.
[61] Ge S S, Tee K P. Approximation-based control of nonlinear MIMO time-delay systems.Automatica,2007,43(1):31-43.
[62] Hua C C, Feng G, Guan X P. Robust controller design of a class of nonlinear time delaysystems via backstepping. Automatica,2008,44(2):567-573.
[63] Jankvic M. Control Lyapunov-Razumikhin functions and robust stabilization of timedelay systems. IEEE Transactions on Automatic Control,2001,46(7):1048-1060.
[64] Xie L, Fridman E, Shaked U. Robust H∞control of distributed delay systems withapplication to the combustion control. IEEE Transactions on Automatic Control),2001,46(12):1930-1935.
[65] Xu S, Chen T. Robust H∞output feedback control for uncertain distributed delay sys-tems, European Journal of Control,2003,9(6):566-574.
[66] Xu S, Chen T. An LMI approach to the H∞filter design for uncertain systems withdistributed delays. IEEE Transactions on Circuits and Systems II,2004,51(4):195-201.
[67] Xu S, Lam J, Chen T, et al. A delay-dependent approach to robust H∞filtering foruncertain distributed delay systems, IEEE Transactions on Signal Processing,2005,53(10):3764-3772.
[68] Yu X G. An LMI approach to robust H∞filtering for uncertain systems with time-varyingdistributed delays. Journal of the Franklin Institute,2008,345(8):877-890.
[69] Tao G, Kokotovic P V. Adaptive sliding control of plants with unknown dead-zone. IEEETransactions on Automatic Control,1994,39(1):59-68.
[70] Tao G, Kokotovic P V. Discrete-time adaptive control of plants with unknown outputdead-zones. Automatica,1995,31(2):287-291.
[71] Zhang T P, Ge S S. Adaptive neural control of MIMO nonlinear state time-varying delaysystems with unknown dead-zones and gain signs. Automatica,2007,32(6):1021-1033.
[72] Zhang T P, Ge S S. Adaptive dynamic surface control of nonlinear systems with unknowndead zone in pure feedback form. Automatica,2008,44(7):1895-1903.
[73]张天平,文慧.基于ISS的非线性纯反馈系统的自适应动态面控制.控制与决策,2009,24(11):1707-1712.
[74] Recker D A, Kokotovic P V, Rhode D, et al. Adaptive nonlinear control of systems con-taining a dead zone. Proceedings of the30th IEEE Conference on Decision and Control,Brighton, England: IEEE Press,1991,2111-115.
[75] Wang X S, Hong H, Su C Y. Robust adaptive control a class of nonlinear systems with anunknown dead-zone. Automatica,2004,40(3):407-413.
[76] Wang Y C, Chien C J, Teng C C. Direct adaptive iterative learning control of nonlinearsystems using an output-recurrent fuzzy neural network. IEEE Transactions on Systems,Man, and Cybernetics, Part B: Cybernetics,2004,34(3):1348-1359.
[77] Ibrir S, Xie W F, Su C Y. Adaptive tracking of nonlinear systems with non-symmetricdead-zone input. Automatica,2007,43(3):522-530.
[78]朱胜,孙明轩,王雪洁,等.具有输入死区的非线性系统的鲁棒重复控制.自动化学报,2013,39(6):908-912.
[79] Selmic R R, Lewis F L. Deadzone compensation in motion control systems using neuralnetworks. IEEE Transactions on Automatic Control,2000,45(4):602-613.
[80] Boulkroune A, MSaad M. Fuzzy adaptive observer-based projective synchronizationfor nonlinear systems with input nonlinearity. Journal of Vibration and Control,2012,18(3):437-450.
[81] Wu X L, Wu X J, Luo X Y, et al. Neural network-based adaptive tracking control fornonlinearly parameterized systems with unknown input nonlinearities. Neurocomputing,2012,82:127-142.
[82] Nussbaum R D. Some remarks on the conjecture in parameter adaptive control. Systems&Control Letters,1983,3(5):242-246.
[83] Wen Y, Ren X. Neural networks-based adaptive control for nonlinear time-varying delayssystems with unknown control direction. EEE Transactions on Neural Networks,2011,22(10):1599-1612.
[84] Ge S S, Hong F, Lee T H. Adaptive neural control of nonlinear time-delay systems withunknown virtual control coefficients. IEEE Transactions on Systems Man Cybernet-PartB,2004,34(1):499-516.
[85] Zhang T P, Ge S S, Xiang C. Output feedback NN control for two classes of discrete-timesystems with unknown control directions in a unified approach. IEEE Transactions onNeural Networks,2008,19(11):1873-1886.
[86] Du H, Ge S S, Liu J K. Adaptive neural network output feedback control for a classof non-affine non-linear systems with unmodelled dynamics. IET Control Theory andApplications,2011,5(3):465-477.
[87] Hong F, Ge S S, Ren B, Lee T H. Robust adaptive control for a class of uncertain strict-feedback nonlinear systems, International Journal of Robust and Nonlinear Control,2009,19(7):746-767.
[88] Boulkroune A, Saad M M, Chekireb H. Design of a fuzzy adaptive controller for MIMOnonlinear time-delay systems with unknown actuator nonlinearities and unknown controldirection. Information Sciences,2010,180(24):5041-5059.
[89] Boulkroune A, Msaad M, Farza M. On the design of observer-based fuzzy adaptivecontroller for nonlinear systems with unknown control gain sign. Fuzzy sets and systems,2012,201(16):71-85.
[90] Liu Y J, Tong S C, Li T S. Observer-based adaptive fuzzy tracking control for a class ofuncertain nonlinear MIMO systems. Fuzzy Sets and Systems,2011,164(1):25–44.
[91] Arslan G, Basar T, Risk-sensitive adaptive trackers for strictfeedback systems with outputmeasurements. IEEE Transations on Automatic Control,2002,47(10):1754-1758.
[92] Chen W S, Zhang L. Adaptive iterative learning control for nonlinearly parameterizedsystems with unknown time-varying delays. International Journal of Control, Automa-tion, and Systems,2010,8(2):177-186.
[93] Deng H, Krstic′M. Stochastic nonlinear stabilization, Part II: Inverse optimality. Systems&Control Letters,1997,32(3):151-159.
[94] Liu Y, Pan Z, Shi S. Output feedback control design for strict feedback stochastic nonlin-ear systems under a risk-sensitive cost. IEEE Transactions on Automatic Control,2003,48(3):509-514.
[95] Liu Y, Zhang J. Practical output feedback risk-sensitive control for stochastic nonlinearsystems under stable zero-dynamics. SIAM Journal on Control and Optimization,2006,45(3):885-926.
[96] Liu S J, Zhang J F, Jiang Z P. Decentralized adaptive output feedback stabilization forlarge-scale stochastic nonlinear systems. Automatica,2007,43(2):238-251.
[97] Mao X. LaSalle-type theorem for stochastic differential delay equations. Journal ofMathematical Analysis and Applications,1999,236(2):350-369.
[98] Mao X. A note on the LaSalle-type theorem for stochastic differential delay equations,Journal of Mathematical Analysis and Applications,2002,268(1):125-142.
[99] Pan Z G, Basar T. Adaptive controller design for tracking and disturbance attenuationin parametric strict-feedback nonlinear systems. IEEE Transactions Automatic Control,1998,43(8):1066-1083.
[100] Tseng C S, Li Y F, Chiang Y F. H∞Fuzzy control design for nonlinear stochastic fuzzysystems. International Journal of Fuzzy Systems,2007,9(1):38-44.
[101] Tian J, Xie X J. Adaptive state-feedback stabilization for high-order stochastic systemswith nonlinear parameterization. Automatica,2009,45(1):126-133.
[102] Xie X J, Tian J. State-feedback stabilization for high-order stochastic nonlinear systemswith stochastic inverse dynamics. International Journal of Robust and Nonlinear Control,2007,17(14):1343-1362.
[103] Tong S C, Li Y, Li Y M, et al. Observer-based adaptive fuzzy backstepping control for aclass of stochastic nonlinear strict-feedback systems. IEEE Transactions on Systems ManCybernetics-Part B: Cybernetics,2011,41(6):1693-1704.
[104] Yu J J, Zhang K J, Fei S M. Adaptive fuzzy tracking control of a class of stochastic non-linear systems with unknown dead-zone Input. International Journal of Fuzzy Systems,2008,10(1):18-23.
[105] Chen W S, Jiao L C, Li J, et al. Adaptive NN backstepping output-feedback control forstochastic nonlinear strict-feedback systems with time-varying delays. IEEE Transactionson Systems, Man, and Cybernetics-Part B: Cybernetics,2010,40(3):939-950.
[106] Yu Z, Jin Z, Du H. Adaptive neural control for a class of non-affine stochastic non-linearsystems with time-varying delay: A Razumikhin-Nussbaum method. IET Control Theoryand Applications,2012,6(1):14-23.
[107] Li Y, Li Y M, Tong S C. Adaptive fuzzy decentralized output feedback control forstochastic nonlinear large-scale systems. Neurocomputing,2012,83:38-46.
[108] Deng H, Krstic′M, Williams R J. Stabilization of stochastic nonlinear systems drivenby noise of unknown covariance. IEEE Transactions on Automatic Control,2001,46(8):1237-1253.
[109] Ji H B, Xi H S. Adaptive output-feedback tracking of stochastic nonlinear systems. IEEETransactions on Automatic Control,2006,51(2):355-360.
[110] Yip P P, Hedrick J K. Adaptive dynamic surface control: a simplified algorithm foradaptive backstepping control of nonlinear systems. International Journal of Control,1998,71(5):959-979.
[111] Swaroop D, Hedrick J K, Yip P P, et al. Dynamic surface control for a class of nonlinearsystems. IEEE Transactions on Automatic Control,2000,45(10):1893-1899.
[112]李红春,张天平,孙研.基于动态面控制的间接自适应神经网络块控制.电机与控制学报,2007,11(3):275-281.
[113] Li T S, Wang D, Feng G, et al. A DSC approach to robust adaptive NN tracking controlfor strict-feedback nonlinear systems. IEEE Trans on Systems, Man and Cybernetics:Cybernetics,2010,40(3):915-927.
[114] Zhang T P, Ge S S. Direct adaptive NN control of nonlinear systems in strict-feedbackform using dynamic surface control. IEEE22nd International Symposium on IntelligentControl,2007,315-320.
[115] Zhang T P, Ge S S. Adaptive neural network tracking control of MIMO nonlinear systemswith unknown dead zones and control directions. IEEE Transactions on neural networks,2009,203:483-497.
[116] Sung J Y, Jin B P, Yoon H C. Adaptive neural control for a class of strict-feedbacknonlinear systems with state time delays. IEEE Transactions on Neural Networks,2009,20(7):1209-1215.
[117] Li Y M, Tong S C, Liu Y J. Adaptive fuzzy dynamic surface control of unknown mul-tivariable nonlinear systems.7th World Congress on Intelligent Control and Automation,2008,4365-4370.
[118] Zhao Q C, Lin Y. Adaptive fuzzy dynamic surface control with prespecified track-ing performance for a class of nonlinear systems. Asian Journal of Control,2011,13(6):1082–1091.
[119] Li T S, Tong S C, et al. A novel robust adaptive-fuzzy tracking control for a class ofnonlinear multi input/multioutput systems. IEEE Transactions on Fuzzy Systems,2010,18(1):150-160.
[120] Li Y M, Li T S, Tong S C. Adaptive fuzzy backstepping dynamic surface control of un-certain nonlinear systems based on filter observer. International Journal of Fuzzy Systems,2012,14(2):320-329.
[121] Tong S C, Li Y M, Jing X J. Adaptive fuzzy decentralized dynamics surface control fornonlinear large-scale systems based on high-gain observer Information Sciences,2013,235(20):287–307.
[122] Chen B, Liu X P, Liu K F, et al. Direct adaptive fuzzy control of nonlinear strict-feedbacksystems. Automatica,2009,45(6):1530-1535.
[123] Li T S, Feng G, Zou Z J, et al. Robust adaptive fuzzy tracking control for a class of MIMOsystems: A minimal-learning-parameters algorithm. American Control Conference,2009,3106-3111.
[124] Liu Y G. Output-feedback adaptive control for a class of nonlinear systems with un-known control directions. Acta Automatica Sinica,2007,33(12):1306-1312.
[125] Li T, Feng G, Wang D, et al. Neural-network-based simple adaptive control of uncertainmulti-input multi-output non-linear systems. IET Control Theory and Applications,2010,4(9):1543-1557.
[126] Li J, Chen W S, Li J M, et al. Adaptive NN output-feedback stabilization for a class ofstrict-feedback stochastic nonlinear systems. ISA Transactions,2009,48(4):468-475.
[127] Karimi H R. Adaptive H∞synchronization of master-slave systems with mixed time-varying delays and nonlinear perturbations: an LMI approach. International Journal ofAutomation and Computing,2011,8(4):381-390.
[128] Liu S J, Ge S Z, Zhang J F. Adaptive output-feedback control for a class of uncertainstochastic nonlinear systems with time delays. International Journal of Control,2008,81(8):1210-1220.
[129] Zhang T P, Yi Y. Adaptive fuzzy control for a class of MIMO nonlinear systems withunknown dead-zones. Acta Automatica Sinica,2007,33(1):96-99.
[130] Chen W S, Zhang Z Q. Globally stable adaptive backstepping fuzzy control for output-feedback systems with unknown high-frequency gain sign. Fuzzy Sets and Systems,2010,161(6):821-836.
[131] Jiang Z, Mareels I, Hill D, Huang J. A unifying framework for global regulation vianonlinear output feedback: From ISS to iISS. IEEE Transactions on Automatic Control.49(4):549-562,2004.
[132] Liu L, Huang J. Global robust output regulation of output feedback systems with un-known high-frequency gain sign. IEEE Transactions Automatic Control,2006,51(4):625-631.
[133] Ryan E P. Nonlinear universal servomechanism. IEEE Transactions Automatic Control,1994,39(4):753-761.
[134] Ye X, Jiang J. Adaptive nonlinear design without a prior knowledge of control directions.IEEE Transactions Automatic Control,1998,43(11):1617-1621.
[135] Lin W, Qian C J. Adaptive Control of Nonlinearly Parameterized Systems: A NonsmoothFeedback Framework. IEEE Transactions on Automatic Control2002,47(5):757-774.
[136] Hua C, Guan X, Shi P. Robust backstepping control for a class of time delayed systems.IEEE Transactions on Automatic Control,2005,50(6):894-899.
[137] Boulkroune A, MSaad M, Farza M. Adaptive fuzzy controller for multivariable nonlinearstate time-varying delay systems subject to input nonlinearities. Fuzzy sets and systems,2011,164(1):45-65.
[138] Chen W S, Jiao L C, Li J, et al. Adaptive NN backstepping output-feedback control forstochastic nonlinear strictfeedback systems with time-varying delays. IEEE Transactionson Systems, Man and Cybernetics-Part B: Cybernetics,2010,40(3):939-950.
[139] Tong S C, H X L, Zhang H G. A combined backstepping and small-gain approach torobust adaptive fuzzy output feedback control. IEEE Transactions on Fuzzy Systems,2009,17(5):1059-1069.
[140] Wang W Y, Chan M L, Lee T T, et al. Recursive backstepping design of an adaptivefuzzy controller for strick output feedback nonlinear systems. Asian Journal of Control,2002,4(3):255-264.
[141] Huang Y S, Wu M. Robust decentralized direct adaptive output feedback fuzzy con-trol for a class of large-sale nonaffine nonlinear systems. Information Sciences,2011,181(11):2392-2404.
[142] Shahnazi R, Pariz N, Kamyad A V. Adaptive fuzzy output feedback control for a classof uncertain nonlinear systems with unknown backlash-like hysteresis. Communicationsin Nonlinear Science and Numerical Simulation,2010,15(8):2206-2221.
[143] Ye X D. Adaptive nonlinear output feedback control with unknown high-frequency gainsign. IEEE Transactions on Automatic Control,2001,46(1):112-115.
[144] Li Y M, Tong S C. Adaptive fuzzy backstepping output feedback control of nonlinearuncertain systems with unknown virtual control coefficients using MT-filters. Neurocom-puting,2011,74(10):1557-1563.
[145] Roh Y, Oh J. Robust stabilization of uncertain input-delay systems by sliding modecontrol with delay compensation. Automatica,1999,35(11):1861-1865.
[146] Mazenc F, Mondie′S, Niculescu S I. Global asymptotic stabilization for chains of inte-grators with a delay in the input. Proceedings of the40th IEEE Conference on Decisionand Contml Orlando, Florida USA,2001,1843-1848.
[147] Mazenc F, Mondie′S, Niculescu S I. Global asymptotic stabilization for chains of integra-tors with a delay in the input. IEEE Transactions on Automatic Control,2003,48(1):57-63.
[148] Zhang X F, Boukas E K, Liu Y G, et al. Asymptotic stabilization of high-order feedfor-ward systems with delays in the input. International Journal of Robust Nonlinear Control,2010,20(12):1395-1406.
[149] Zhu Q, Zhang T P, Fei S M. Adaptive tracking control for input delayed MIMO onlinearsystems. Neurocomputing,2010,74(1-3):472-480.
[150] Tong S C, Li Y, Feng G, et al. Observer-based adaptive fuzzy backstepping dynamicsurface control for a class of nonlinear systems with unknown time delays. IET ControlTheory and Applications,2011,5(12):1426–1438.
[151] Chen W S, Li R H. Adaptive output-feedback control for MIMO nonlinear systemswith timevarying delays using neural networks. Journal of Systems Engineering andElectronics,21(5):850-858,2010.
[152] Chen M, Jiang C S, Wu Q X. Backstepping control for a class of uncertain nonlin-ear systems with neural network. International Journal of Nonlinear Science,2007,3(2):137-143.
[153] Ho D W C, Li J M, Niu Y G. Adaptive neural control for a class of nonlinear parametrictime delays systems. IEEE Transactions on Neural Networks,2005,16(3):625-635.
[154] Li Y, Qiang S, Zhuang X Y, Kaynak O. Robust and adaptive backstepping control fornonlinear systems using RBF neural networks. IEEE Trans. on Neural Networks,2004,15(3):693-701.
[155] Li Y M, Tong S C, Li T S. Adaptive fuzzy output feedback control of uncertain nonlinearsystems with unknown backlash-like hysteresis. Information Sciences,2012,198(1):130-146.
[156] Li Y, Tong S C, Li Y M. Observer-based adaptive fuzzy backstepping control of MIMOstochastic nonlinear strict-feedback systems. Nonlinear Dynamics,2012,67(2):1579-1593.
[157] Lee H. Robust Adaptive fuzzy control by backstepping for a class of MIMO nonlinearsystems. IEEE Transactions on Fuzzy Systems,2011,19(2):265-275.
[158] Tong S C, Liu C L, Li Y M. Fuzzy-adaptive decentralized output-feedback control forlarge-scale nonlinear systems with dynamical uncertainties. IEEE Transactions on FuzzySystems,2010,18(5):845-861.
[159] Tong S C, Li Y M, Xia Y Q, et al. Adaptive fuzzy backstepping output feedback controlof nonlinear time-delay systems with unknown high-frequency gain sign. InternationalJournal of Automation and Computing,2011,8(1):14-22.
[160] Tong S C, Sheng N. Adaptive fuzzy observer backstepping control for a class of uncertainnonlinear systems with unknown time-delay. International Journal of Automation andComputing,2010,7(2):236-246.
[161] Tong S C, Li Y M, Shi P. Observer-based adaptive fuzzy backstepping output feed-back control of uncertain MIMO pure-feedback nonlinear systems. IEEE Transactionson Fuzzy Systems,2012,20(4):771-785.
[162] Tong S C, Ren C E, Li Y M. Adaptive fuzzy decentralized control for nonlinear large-scale systems based on high-gain observer. Science China Information Sciences,2012,55(1):228-242.
[163] Zhou J, Er M J, Zurada J M. Adaptive neural network control of uncertain nonlinearsystems with nonsmooth actuator nonlinearities. Neurocomputing,2007,70:1062–1070.
[164] Swaroop D, Gerdes J C, Yip P P, et al. Dynamic surface control of nonlinear systems.Proceedings of American Control Conference, Albuquerque, NM, U.S.A.,1997,3028-3034.
[165] Wang D, Huang J. Neural network based adaptive dynamic surface control for non-linear systems in strict-feedback form. IEEE Transactions on Neural Networks,2005,16(1):195-202.
[166] Chen W S. Adaptive backstepping dynamic surface control for systems with peri-odic disturbances using neural networks. IET Control Theory and Applications,2009,3(10):1383–1394.
[167] Han S I, Lee J M. Adaptive dynamic surface control with sliding mode controland RWNN for robust positioning of a linear motion stage. Mechatronics,2012,22(2):222–238.
[168] Wang M, Liu X P, Shi P. Adaptive neural control of pure-feedback nonlinear time-delay systems via dynamic surface technique. IEEE Transactions on Systems, Man, andCybernetics-part B: Cybernetics,2011,41(6):1681-1692.
[169] Yoo S J, Park J B. Neural-network-based decentralized adaptive control for a class oflarge-scale nonlinear systems with unknown timevarying delays. IEEE Transactions onSystems, Man, and Cybernetics-Part B: Cybernetics,2009,39(5):1316-1323.
[170] Tong S C, Li Y M, Feng G, et al. Observer-based adaptive fuzzy backstepping dynamicsurface control for a class of MIMO nonlinear systems. IEEE Transactions on Systems,Man, and Cybernetics-Part B: Cybernetics,2011,41(4):1124-1135.
[171] Lin Z, Fang H. On asymptotic stabilizabity of linear systems with delayed input, IEEETransactions on Automatic Control,2007,52(6):998-1013.
[172] Mazenc F, Niculescu S I, Bekaik M. Backstepping for nonlinear systems with delay inthe input revisited. SIAM Journal on Control and Optimization,2011,49(6):2263-2278.
[173] Hale J.K. and Lunel S.M. Introduction to Functional Differential Equations. Springer-Verlag, New York, USA,1993.
[174] Khasminskii R. Z. Stochastic Stability of Differential Equations, Rockville, MD: Sijthoffand Noordhoff,1980.
[2] Zadeh L A. Outline of a new approach to the analysis of complex systems and decisionprocesses[J]. IEEE Transactions on Systems, Man, Cybernetics,1973,3(1):28-44.
[3] Mamdani E H. Applications of fuzzy algorithms for simple dynamic plant. Proc. IEEControl and Science,1974,121(12):1585-1588.
[4] Procyk T J, Mamdani E H. A linguistic self-organizing process controller. Automatica,1979,15(1):15-30.
[5]李江荣.模糊系统的广义H2控制. PhD thesis,西安,西安电子科技大学,2012.
[6] Takagi T, Sugeno M. Fuzzy identification of systems and its applications to modeling andcontrol. IEEE Transactions on Systems, Man, Cybern. B: Cybernetics,1985,15(1):116-132.
[7]王立新.自适应模糊系统与控制–设计与稳定性分析.北京:国防工业出版社,1995.
[8] Wang L X. Adaptive fuzzy systems and control:design and stability analysis. Prentice-Hall, EnglewoodCliffs, NJ,1994.
[9] Kokotivic P V, Arcak M. Constructive nonlinear control: A historical perspective. Auto-matica,2007,37(3):637-662.
[10] Byrnes C I, Isidori A. New results and examples in nonlinear feedback stabilization.Systems and Control Letters,1989,12(5):437-442.
[11] Kokotivic P V, Sussmann H J. Posivite real condition for global stabilization of nonlinearsystems. Systems and Control Letters,1989,12(2):125-133.
[12] Saberi A, Kokotivic P V, Sussmann H J. Global stabilization of partially linear compositesystems. SIAM Journal of Control and Optimization,1990,28(6):1491-1503.
[13]胡跃明.非线性控制系统理论与应用.北京:国防工业出版社,2002.
[14]宫琪,田玉平.非线性交叉严格反馈系统的一种构造性设计方法.自动化学报,2000,26(4):447-453.
[15] Krstic′M, Kanellakopoulos I, Kokotovic P V. Nonlinear and adaptive control design.New York:Wiley,1995.
[16] Kanellakopoulos I, Kokotovic P V, Morse A S. Systematic design of adaptive con-trollers for feedback linearizable systems. IEEE Transactions on Automatic Control,1991,36(11):1241-1253.
[17] Marino R, Tomei P. Global adaptive output-feedback control of nonlinear systems, I:Linear parameterization. IEEE Transactions on Automatic Control,1993,38(1):17-32.
[18] Marino R, Tomei P. Robust stabilization of feedback linearizable time-varying uncertainnonlinear systems. Automatica,1993,29(1):181-189.
[19] Yao B, Tomizuka M. Adaptive robust control of SISO nonlinear systems in a semi-strictfeedback form. Automatica,1997,33(5):893-900.
[20]陈为胜.非线性系统智能Backstepping控制与分析. PhD thesis,西安,西安电子科技大学,2007.
[21] Krstic′M, Deng H. Stabilization of Nonlinear Uncertain Systems, London, U.K.:Springer-Verlag,1998.
[22] Boulkroune A, Tadjine M, Saad M, et al. How to design a fuzzy adaptive controllerbased on observers for uncertain affine nonlinear systems. Fuzzy Sets and Systems,2008,159(8)926–948.
[23] Golea N, Golea A, Benmahammed K. Stable indirect fuzzy adaptive control. Fuzzy Setsand Systems,2003,137(3):353–366.
[24] Golea N, Golea A, Barra K. Observer-based adaptive control of robot manipulators: fuzzysystems approach. Applied Soft Computing,2008,8(1):778–787.
[25] Tong S C, Chai T Y. Fuzzy adaptive control for a class of nonlinear systems. Fuzzy Setsand Systems,1999,101(1):31–39.
[26] Wang W Y, Chan M L, Lee T T, et al. Adaptive fuzzy control for strict-feedback canon-ical nonlinear systems with H∞tracking performance. IEEE Transactions on Systems,Man,and Cybernetics―PartB,2000,30(6):878–885.
[27] Chang Y C. Robust tracking control for nonlinear MIMO systems via fuzzy approaches.Automatica,2000,36(10):1535–1545.
[28] Chang Y C. Adaptive fuzzy-based tracking control for nonlinear SISO systems via VSSand H∞approaches. IEEE Transactions on Fuzzy Systems,2001,9(2):278–292.
[29] Chen B S, Lee C H, Chang Y C. H∞tracking design of uncertain nonlinear SISO systems:adaptive fuzzy approach. IEEE Transactions on Fuzzy Systems,1996,4(1):32–43.
[30] Spooner J T, Passino K V. Stable adaptive control using fuzzy systems and neural net-works. IEEE Transaction on Fuzzy Systems,1996,4(3):339–359.
[31] Su C Y, Stepanenko Y. Adaptive control of a class of nonlinear systems with fuzzy logic.IEEE Transactions on Fuzzy Systems,1994,2(4):285–294.
[32] Wang L X. Stable adaptive fuzzy control of nonlinear systems. IEEE Transactions onFuzzy Systems,1993,1(2):146–155.
[33] Zou A M, Kumar K D. Adaptive fuzzy fault-tolerant attitude control of spacecraft. Con-trol Engineering Practice,2011,19(1):10-212.
[34] Jagannnathan S, Lewis F L. Robust backstepping control of a class of nonlinear systemsusing fuzzy logic. Information Sciences,2000,123(3):223–240.
[35] Tong S C, Li Y, Shi P. Fuzzy adaptive backstepping robust control for SISO nonlinearsystems with dynamic uncertainties. Information Sciences,2009,179(9):1319–1332.
[36] Wang M, Chen B. Direct adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear systems. Fuzzy Sets and Systems,2007,158(24):2655–2670.
[37] Wang M, Chen B, Shi P. Adaptive neural control for a class of perturbed strict-feedbacknonlinear time-delay systems. IEEE Transactions on Systems, Man, and Cybernet-ics―PartB,2008,38(3):721–730.
[38] Tong S C, Li Y M. Observer-based fuzzy adaptive control for strict-feedback nonlinearsystems. Fuzzy Sets and Systems,2009,160(12):1749–1764
[39] Tong S C, Li Y M. Observer-based fuzzy adaptive robust control of nonlinear systemswith time delays and unmodeled dynamics. Neurocomputing,2010,74(1):369–378
[40] Zhou S S, Feng G, Feng C B. Robust control for a class of uncertain nonlinear sys-tems:adaptive fuzzy approach based on backstepping, Fuzzy Sets and Systems.2005,151(1):1-20.
[41] Li C Y, Tong S C, Wang W. Fuzzy adaptive high-gain-based observer backstepping con-trol for SISO nonlinear systems. Information Sciences,2011,181(11):2405–2421.
[42] Chen W S, Jiao L C, Li R H, et al. Adaptive Backstepping Fuzzy Control for Nonlin-early Parameterized Systems With Periodic Disturbances. IEEE Transactions on FuzzySystems,2010,18(4):674-685.
[43] Yang Y S. Direct robust adaptive fuzzy control(DRAFC) for uncertain nonlinear systemsusing small-gain theorem. Fuzzy Sets and Systems,2005,151(1):79–97.
[44] Yang Y S, Zhou C J. Adaptive fuzzy H∞stabilization for strict-feedback canonical non-linear systems via backstepping and small-gain approach. IEEE Transactions on FuzzySystems,2005,13(1):104-114.
[45] Chen B, Liu X P, Shi P. Comment on“adaptive fuzzy H∞stabilization for strict-feedback canonical nonlinear systems via backstepping and small-gain approach”. IEEETransactions on Fuzzy Systems,2009,17(3):732–733.
[46] Tong S C, He X L, Li Y M, et al. Adaptive fuzzy backstepping robust control for un-certain nonlinear systems based on small-gainapproach. Fuzzy Sets and Systems2010,161(6):771-796.
[47] Tong S C, He X L, Li Y M. Direct adaptive fuzzy backstepping robust control for singleinput and single output uncertain nonlinear systems using small-gain approach. Informa-tion Sciences,2010,180(9):1738–1758.
[48] Chen B, Liu X P, Tong S C. Fuzzy approximate disturbance decoupling of MIMO nonlin-ear systems by backstepping and application to chemical processes. IEEE Transactionson Fuzzy Systems,2005,13(6):832–847.
[49] Chen B, Liu X P, Tong S C. Fuzzy approximate disturbance decoupling of MIMO non-linear systems by backstepping approach. Fuzzy Sets and Systems,2007,158(10):1097-1125.
[50] Tong S C, Li C Y, Li Y M. Fuzzy adaptive observer backstepping control for MIMOnonlinear systems. Fuzzy Sets and Systems,2009,160(19):2755-2775.
[51] Yousef H, Hamdy M, El-Madbouly E, et al. Adaptive fuzzy decentralized control forinterconnected MIMO nonlinear subsystems. Automatica,2009,45(2):456-462.
[52] Liu Y J, Tong S C, Wang W. Adaptive fuzzy output tracking control for a class of uncer-tain nonlinear systems. Fuzzy Sets and Systems,2009,160(19):2727–2754.
[53] Niculescu S L. Delay Effects on Stability: A Robust Control Approach. Springer, London,2001.
[54] Boukas E K, Al-Muthairi N F. Delay-dependent stabilization of singular linear systemswith delays. International Journal of Innovative Computing, Information and Control,2006,2(2):283–291.
[55] Chen B, Lam J, Xu S. Memory state feedback guaranteed cost control for neutral delaysystems. International Journal of Innovative Computing, Information and Control,2006,2(2):293–303.
[56] Wang M, Chen B, Liu X P, et al. Adaptive fuzzy tracking control for a class of perturbedstrict-feedback nonlinear time-delay systems. Fuzzy Sets and Systems,2008,159(8):949-967.
[57] Wang M, Chen B, Liu K F, et al. Adaptive fuzzy tracking control of nonlinear time-delay systems with unknown virtual control coefficients. Information Sciences,2008,178(22):4326–4340.
[58] Wang M, Chen B, Tong S C. Adaptive fuzzy tracking control for strict-feedback nonlin-ear systems with unknown time delays. International Journal of Innovative Computing,Information and Control,2008,4(4):829-838.
[59] Chen B, Liu X P, Liu K F, et al. Direct adaptive fuzzy control for nonlinear systems withtime-varying delays. Information Sciences,2010,180(5):776-792.
[60] Hua C C, Wang Q G, Guan X P. Adaptive fuzzy output-feedback controller design fornonlinear time-delay systems with unknown control direction. IEEE Transactions onSystems Man Cybernet-Part B,2009,39(2):363-374.
[61] Ge S S, Tee K P. Approximation-based control of nonlinear MIMO time-delay systems.Automatica,2007,43(1):31-43.
[62] Hua C C, Feng G, Guan X P. Robust controller design of a class of nonlinear time delaysystems via backstepping. Automatica,2008,44(2):567-573.
[63] Jankvic M. Control Lyapunov-Razumikhin functions and robust stabilization of timedelay systems. IEEE Transactions on Automatic Control,2001,46(7):1048-1060.
[64] Xie L, Fridman E, Shaked U. Robust H∞control of distributed delay systems withapplication to the combustion control. IEEE Transactions on Automatic Control),2001,46(12):1930-1935.
[65] Xu S, Chen T. Robust H∞output feedback control for uncertain distributed delay sys-tems, European Journal of Control,2003,9(6):566-574.
[66] Xu S, Chen T. An LMI approach to the H∞filter design for uncertain systems withdistributed delays. IEEE Transactions on Circuits and Systems II,2004,51(4):195-201.
[67] Xu S, Lam J, Chen T, et al. A delay-dependent approach to robust H∞filtering foruncertain distributed delay systems, IEEE Transactions on Signal Processing,2005,53(10):3764-3772.
[68] Yu X G. An LMI approach to robust H∞filtering for uncertain systems with time-varyingdistributed delays. Journal of the Franklin Institute,2008,345(8):877-890.
[69] Tao G, Kokotovic P V. Adaptive sliding control of plants with unknown dead-zone. IEEETransactions on Automatic Control,1994,39(1):59-68.
[70] Tao G, Kokotovic P V. Discrete-time adaptive control of plants with unknown outputdead-zones. Automatica,1995,31(2):287-291.
[71] Zhang T P, Ge S S. Adaptive neural control of MIMO nonlinear state time-varying delaysystems with unknown dead-zones and gain signs. Automatica,2007,32(6):1021-1033.
[72] Zhang T P, Ge S S. Adaptive dynamic surface control of nonlinear systems with unknowndead zone in pure feedback form. Automatica,2008,44(7):1895-1903.
[73]张天平,文慧.基于ISS的非线性纯反馈系统的自适应动态面控制.控制与决策,2009,24(11):1707-1712.
[74] Recker D A, Kokotovic P V, Rhode D, et al. Adaptive nonlinear control of systems con-taining a dead zone. Proceedings of the30th IEEE Conference on Decision and Control,Brighton, England: IEEE Press,1991,2111-115.
[75] Wang X S, Hong H, Su C Y. Robust adaptive control a class of nonlinear systems with anunknown dead-zone. Automatica,2004,40(3):407-413.
[76] Wang Y C, Chien C J, Teng C C. Direct adaptive iterative learning control of nonlinearsystems using an output-recurrent fuzzy neural network. IEEE Transactions on Systems,Man, and Cybernetics, Part B: Cybernetics,2004,34(3):1348-1359.
[77] Ibrir S, Xie W F, Su C Y. Adaptive tracking of nonlinear systems with non-symmetricdead-zone input. Automatica,2007,43(3):522-530.
[78]朱胜,孙明轩,王雪洁,等.具有输入死区的非线性系统的鲁棒重复控制.自动化学报,2013,39(6):908-912.
[79] Selmic R R, Lewis F L. Deadzone compensation in motion control systems using neuralnetworks. IEEE Transactions on Automatic Control,2000,45(4):602-613.
[80] Boulkroune A, MSaad M. Fuzzy adaptive observer-based projective synchronizationfor nonlinear systems with input nonlinearity. Journal of Vibration and Control,2012,18(3):437-450.
[81] Wu X L, Wu X J, Luo X Y, et al. Neural network-based adaptive tracking control fornonlinearly parameterized systems with unknown input nonlinearities. Neurocomputing,2012,82:127-142.
[82] Nussbaum R D. Some remarks on the conjecture in parameter adaptive control. Systems&Control Letters,1983,3(5):242-246.
[83] Wen Y, Ren X. Neural networks-based adaptive control for nonlinear time-varying delayssystems with unknown control direction. EEE Transactions on Neural Networks,2011,22(10):1599-1612.
[84] Ge S S, Hong F, Lee T H. Adaptive neural control of nonlinear time-delay systems withunknown virtual control coefficients. IEEE Transactions on Systems Man Cybernet-PartB,2004,34(1):499-516.
[85] Zhang T P, Ge S S, Xiang C. Output feedback NN control for two classes of discrete-timesystems with unknown control directions in a unified approach. IEEE Transactions onNeural Networks,2008,19(11):1873-1886.
[86] Du H, Ge S S, Liu J K. Adaptive neural network output feedback control for a classof non-affine non-linear systems with unmodelled dynamics. IET Control Theory andApplications,2011,5(3):465-477.
[87] Hong F, Ge S S, Ren B, Lee T H. Robust adaptive control for a class of uncertain strict-feedback nonlinear systems, International Journal of Robust and Nonlinear Control,2009,19(7):746-767.
[88] Boulkroune A, Saad M M, Chekireb H. Design of a fuzzy adaptive controller for MIMOnonlinear time-delay systems with unknown actuator nonlinearities and unknown controldirection. Information Sciences,2010,180(24):5041-5059.
[89] Boulkroune A, Msaad M, Farza M. On the design of observer-based fuzzy adaptivecontroller for nonlinear systems with unknown control gain sign. Fuzzy sets and systems,2012,201(16):71-85.
[90] Liu Y J, Tong S C, Li T S. Observer-based adaptive fuzzy tracking control for a class ofuncertain nonlinear MIMO systems. Fuzzy Sets and Systems,2011,164(1):25–44.
[91] Arslan G, Basar T, Risk-sensitive adaptive trackers for strictfeedback systems with outputmeasurements. IEEE Transations on Automatic Control,2002,47(10):1754-1758.
[92] Chen W S, Zhang L. Adaptive iterative learning control for nonlinearly parameterizedsystems with unknown time-varying delays. International Journal of Control, Automa-tion, and Systems,2010,8(2):177-186.
[93] Deng H, Krstic′M. Stochastic nonlinear stabilization, Part II: Inverse optimality. Systems&Control Letters,1997,32(3):151-159.
[94] Liu Y, Pan Z, Shi S. Output feedback control design for strict feedback stochastic nonlin-ear systems under a risk-sensitive cost. IEEE Transactions on Automatic Control,2003,48(3):509-514.
[95] Liu Y, Zhang J. Practical output feedback risk-sensitive control for stochastic nonlinearsystems under stable zero-dynamics. SIAM Journal on Control and Optimization,2006,45(3):885-926.
[96] Liu S J, Zhang J F, Jiang Z P. Decentralized adaptive output feedback stabilization forlarge-scale stochastic nonlinear systems. Automatica,2007,43(2):238-251.
[97] Mao X. LaSalle-type theorem for stochastic differential delay equations. Journal ofMathematical Analysis and Applications,1999,236(2):350-369.
[98] Mao X. A note on the LaSalle-type theorem for stochastic differential delay equations,Journal of Mathematical Analysis and Applications,2002,268(1):125-142.
[99] Pan Z G, Basar T. Adaptive controller design for tracking and disturbance attenuationin parametric strict-feedback nonlinear systems. IEEE Transactions Automatic Control,1998,43(8):1066-1083.
[100] Tseng C S, Li Y F, Chiang Y F. H∞Fuzzy control design for nonlinear stochastic fuzzysystems. International Journal of Fuzzy Systems,2007,9(1):38-44.
[101] Tian J, Xie X J. Adaptive state-feedback stabilization for high-order stochastic systemswith nonlinear parameterization. Automatica,2009,45(1):126-133.
[102] Xie X J, Tian J. State-feedback stabilization for high-order stochastic nonlinear systemswith stochastic inverse dynamics. International Journal of Robust and Nonlinear Control,2007,17(14):1343-1362.
[103] Tong S C, Li Y, Li Y M, et al. Observer-based adaptive fuzzy backstepping control for aclass of stochastic nonlinear strict-feedback systems. IEEE Transactions on Systems ManCybernetics-Part B: Cybernetics,2011,41(6):1693-1704.
[104] Yu J J, Zhang K J, Fei S M. Adaptive fuzzy tracking control of a class of stochastic non-linear systems with unknown dead-zone Input. International Journal of Fuzzy Systems,2008,10(1):18-23.
[105] Chen W S, Jiao L C, Li J, et al. Adaptive NN backstepping output-feedback control forstochastic nonlinear strict-feedback systems with time-varying delays. IEEE Transactionson Systems, Man, and Cybernetics-Part B: Cybernetics,2010,40(3):939-950.
[106] Yu Z, Jin Z, Du H. Adaptive neural control for a class of non-affine stochastic non-linearsystems with time-varying delay: A Razumikhin-Nussbaum method. IET Control Theoryand Applications,2012,6(1):14-23.
[107] Li Y, Li Y M, Tong S C. Adaptive fuzzy decentralized output feedback control forstochastic nonlinear large-scale systems. Neurocomputing,2012,83:38-46.
[108] Deng H, Krstic′M, Williams R J. Stabilization of stochastic nonlinear systems drivenby noise of unknown covariance. IEEE Transactions on Automatic Control,2001,46(8):1237-1253.
[109] Ji H B, Xi H S. Adaptive output-feedback tracking of stochastic nonlinear systems. IEEETransactions on Automatic Control,2006,51(2):355-360.
[110] Yip P P, Hedrick J K. Adaptive dynamic surface control: a simplified algorithm foradaptive backstepping control of nonlinear systems. International Journal of Control,1998,71(5):959-979.
[111] Swaroop D, Hedrick J K, Yip P P, et al. Dynamic surface control for a class of nonlinearsystems. IEEE Transactions on Automatic Control,2000,45(10):1893-1899.
[112]李红春,张天平,孙研.基于动态面控制的间接自适应神经网络块控制.电机与控制学报,2007,11(3):275-281.
[113] Li T S, Wang D, Feng G, et al. A DSC approach to robust adaptive NN tracking controlfor strict-feedback nonlinear systems. IEEE Trans on Systems, Man and Cybernetics:Cybernetics,2010,40(3):915-927.
[114] Zhang T P, Ge S S. Direct adaptive NN control of nonlinear systems in strict-feedbackform using dynamic surface control. IEEE22nd International Symposium on IntelligentControl,2007,315-320.
[115] Zhang T P, Ge S S. Adaptive neural network tracking control of MIMO nonlinear systemswith unknown dead zones and control directions. IEEE Transactions on neural networks,2009,203:483-497.
[116] Sung J Y, Jin B P, Yoon H C. Adaptive neural control for a class of strict-feedbacknonlinear systems with state time delays. IEEE Transactions on Neural Networks,2009,20(7):1209-1215.
[117] Li Y M, Tong S C, Liu Y J. Adaptive fuzzy dynamic surface control of unknown mul-tivariable nonlinear systems.7th World Congress on Intelligent Control and Automation,2008,4365-4370.
[118] Zhao Q C, Lin Y. Adaptive fuzzy dynamic surface control with prespecified track-ing performance for a class of nonlinear systems. Asian Journal of Control,2011,13(6):1082–1091.
[119] Li T S, Tong S C, et al. A novel robust adaptive-fuzzy tracking control for a class ofnonlinear multi input/multioutput systems. IEEE Transactions on Fuzzy Systems,2010,18(1):150-160.
[120] Li Y M, Li T S, Tong S C. Adaptive fuzzy backstepping dynamic surface control of un-certain nonlinear systems based on filter observer. International Journal of Fuzzy Systems,2012,14(2):320-329.
[121] Tong S C, Li Y M, Jing X J. Adaptive fuzzy decentralized dynamics surface control fornonlinear large-scale systems based on high-gain observer Information Sciences,2013,235(20):287–307.
[122] Chen B, Liu X P, Liu K F, et al. Direct adaptive fuzzy control of nonlinear strict-feedbacksystems. Automatica,2009,45(6):1530-1535.
[123] Li T S, Feng G, Zou Z J, et al. Robust adaptive fuzzy tracking control for a class of MIMOsystems: A minimal-learning-parameters algorithm. American Control Conference,2009,3106-3111.
[124] Liu Y G. Output-feedback adaptive control for a class of nonlinear systems with un-known control directions. Acta Automatica Sinica,2007,33(12):1306-1312.
[125] Li T, Feng G, Wang D, et al. Neural-network-based simple adaptive control of uncertainmulti-input multi-output non-linear systems. IET Control Theory and Applications,2010,4(9):1543-1557.
[126] Li J, Chen W S, Li J M, et al. Adaptive NN output-feedback stabilization for a class ofstrict-feedback stochastic nonlinear systems. ISA Transactions,2009,48(4):468-475.
[127] Karimi H R. Adaptive H∞synchronization of master-slave systems with mixed time-varying delays and nonlinear perturbations: an LMI approach. International Journal ofAutomation and Computing,2011,8(4):381-390.
[128] Liu S J, Ge S Z, Zhang J F. Adaptive output-feedback control for a class of uncertainstochastic nonlinear systems with time delays. International Journal of Control,2008,81(8):1210-1220.
[129] Zhang T P, Yi Y. Adaptive fuzzy control for a class of MIMO nonlinear systems withunknown dead-zones. Acta Automatica Sinica,2007,33(1):96-99.
[130] Chen W S, Zhang Z Q. Globally stable adaptive backstepping fuzzy control for output-feedback systems with unknown high-frequency gain sign. Fuzzy Sets and Systems,2010,161(6):821-836.
[131] Jiang Z, Mareels I, Hill D, Huang J. A unifying framework for global regulation vianonlinear output feedback: From ISS to iISS. IEEE Transactions on Automatic Control.49(4):549-562,2004.
[132] Liu L, Huang J. Global robust output regulation of output feedback systems with un-known high-frequency gain sign. IEEE Transactions Automatic Control,2006,51(4):625-631.
[133] Ryan E P. Nonlinear universal servomechanism. IEEE Transactions Automatic Control,1994,39(4):753-761.
[134] Ye X, Jiang J. Adaptive nonlinear design without a prior knowledge of control directions.IEEE Transactions Automatic Control,1998,43(11):1617-1621.
[135] Lin W, Qian C J. Adaptive Control of Nonlinearly Parameterized Systems: A NonsmoothFeedback Framework. IEEE Transactions on Automatic Control2002,47(5):757-774.
[136] Hua C, Guan X, Shi P. Robust backstepping control for a class of time delayed systems.IEEE Transactions on Automatic Control,2005,50(6):894-899.
[137] Boulkroune A, MSaad M, Farza M. Adaptive fuzzy controller for multivariable nonlinearstate time-varying delay systems subject to input nonlinearities. Fuzzy sets and systems,2011,164(1):45-65.
[138] Chen W S, Jiao L C, Li J, et al. Adaptive NN backstepping output-feedback control forstochastic nonlinear strictfeedback systems with time-varying delays. IEEE Transactionson Systems, Man and Cybernetics-Part B: Cybernetics,2010,40(3):939-950.
[139] Tong S C, H X L, Zhang H G. A combined backstepping and small-gain approach torobust adaptive fuzzy output feedback control. IEEE Transactions on Fuzzy Systems,2009,17(5):1059-1069.
[140] Wang W Y, Chan M L, Lee T T, et al. Recursive backstepping design of an adaptivefuzzy controller for strick output feedback nonlinear systems. Asian Journal of Control,2002,4(3):255-264.
[141] Huang Y S, Wu M. Robust decentralized direct adaptive output feedback fuzzy con-trol for a class of large-sale nonaffine nonlinear systems. Information Sciences,2011,181(11):2392-2404.
[142] Shahnazi R, Pariz N, Kamyad A V. Adaptive fuzzy output feedback control for a classof uncertain nonlinear systems with unknown backlash-like hysteresis. Communicationsin Nonlinear Science and Numerical Simulation,2010,15(8):2206-2221.
[143] Ye X D. Adaptive nonlinear output feedback control with unknown high-frequency gainsign. IEEE Transactions on Automatic Control,2001,46(1):112-115.
[144] Li Y M, Tong S C. Adaptive fuzzy backstepping output feedback control of nonlinearuncertain systems with unknown virtual control coefficients using MT-filters. Neurocom-puting,2011,74(10):1557-1563.
[145] Roh Y, Oh J. Robust stabilization of uncertain input-delay systems by sliding modecontrol with delay compensation. Automatica,1999,35(11):1861-1865.
[146] Mazenc F, Mondie′S, Niculescu S I. Global asymptotic stabilization for chains of inte-grators with a delay in the input. Proceedings of the40th IEEE Conference on Decisionand Contml Orlando, Florida USA,2001,1843-1848.
[147] Mazenc F, Mondie′S, Niculescu S I. Global asymptotic stabilization for chains of integra-tors with a delay in the input. IEEE Transactions on Automatic Control,2003,48(1):57-63.
[148] Zhang X F, Boukas E K, Liu Y G, et al. Asymptotic stabilization of high-order feedfor-ward systems with delays in the input. International Journal of Robust Nonlinear Control,2010,20(12):1395-1406.
[149] Zhu Q, Zhang T P, Fei S M. Adaptive tracking control for input delayed MIMO onlinearsystems. Neurocomputing,2010,74(1-3):472-480.
[150] Tong S C, Li Y, Feng G, et al. Observer-based adaptive fuzzy backstepping dynamicsurface control for a class of nonlinear systems with unknown time delays. IET ControlTheory and Applications,2011,5(12):1426–1438.
[151] Chen W S, Li R H. Adaptive output-feedback control for MIMO nonlinear systemswith timevarying delays using neural networks. Journal of Systems Engineering andElectronics,21(5):850-858,2010.
[152] Chen M, Jiang C S, Wu Q X. Backstepping control for a class of uncertain nonlin-ear systems with neural network. International Journal of Nonlinear Science,2007,3(2):137-143.
[153] Ho D W C, Li J M, Niu Y G. Adaptive neural control for a class of nonlinear parametrictime delays systems. IEEE Transactions on Neural Networks,2005,16(3):625-635.
[154] Li Y, Qiang S, Zhuang X Y, Kaynak O. Robust and adaptive backstepping control fornonlinear systems using RBF neural networks. IEEE Trans. on Neural Networks,2004,15(3):693-701.
[155] Li Y M, Tong S C, Li T S. Adaptive fuzzy output feedback control of uncertain nonlinearsystems with unknown backlash-like hysteresis. Information Sciences,2012,198(1):130-146.
[156] Li Y, Tong S C, Li Y M. Observer-based adaptive fuzzy backstepping control of MIMOstochastic nonlinear strict-feedback systems. Nonlinear Dynamics,2012,67(2):1579-1593.
[157] Lee H. Robust Adaptive fuzzy control by backstepping for a class of MIMO nonlinearsystems. IEEE Transactions on Fuzzy Systems,2011,19(2):265-275.
[158] Tong S C, Liu C L, Li Y M. Fuzzy-adaptive decentralized output-feedback control forlarge-scale nonlinear systems with dynamical uncertainties. IEEE Transactions on FuzzySystems,2010,18(5):845-861.
[159] Tong S C, Li Y M, Xia Y Q, et al. Adaptive fuzzy backstepping output feedback controlof nonlinear time-delay systems with unknown high-frequency gain sign. InternationalJournal of Automation and Computing,2011,8(1):14-22.
[160] Tong S C, Sheng N. Adaptive fuzzy observer backstepping control for a class of uncertainnonlinear systems with unknown time-delay. International Journal of Automation andComputing,2010,7(2):236-246.
[161] Tong S C, Li Y M, Shi P. Observer-based adaptive fuzzy backstepping output feed-back control of uncertain MIMO pure-feedback nonlinear systems. IEEE Transactionson Fuzzy Systems,2012,20(4):771-785.
[162] Tong S C, Ren C E, Li Y M. Adaptive fuzzy decentralized control for nonlinear large-scale systems based on high-gain observer. Science China Information Sciences,2012,55(1):228-242.
[163] Zhou J, Er M J, Zurada J M. Adaptive neural network control of uncertain nonlinearsystems with nonsmooth actuator nonlinearities. Neurocomputing,2007,70:1062–1070.
[164] Swaroop D, Gerdes J C, Yip P P, et al. Dynamic surface control of nonlinear systems.Proceedings of American Control Conference, Albuquerque, NM, U.S.A.,1997,3028-3034.
[165] Wang D, Huang J. Neural network based adaptive dynamic surface control for non-linear systems in strict-feedback form. IEEE Transactions on Neural Networks,2005,16(1):195-202.
[166] Chen W S. Adaptive backstepping dynamic surface control for systems with peri-odic disturbances using neural networks. IET Control Theory and Applications,2009,3(10):1383–1394.
[167] Han S I, Lee J M. Adaptive dynamic surface control with sliding mode controland RWNN for robust positioning of a linear motion stage. Mechatronics,2012,22(2):222–238.
[168] Wang M, Liu X P, Shi P. Adaptive neural control of pure-feedback nonlinear time-delay systems via dynamic surface technique. IEEE Transactions on Systems, Man, andCybernetics-part B: Cybernetics,2011,41(6):1681-1692.
[169] Yoo S J, Park J B. Neural-network-based decentralized adaptive control for a class oflarge-scale nonlinear systems with unknown timevarying delays. IEEE Transactions onSystems, Man, and Cybernetics-Part B: Cybernetics,2009,39(5):1316-1323.
[170] Tong S C, Li Y M, Feng G, et al. Observer-based adaptive fuzzy backstepping dynamicsurface control for a class of MIMO nonlinear systems. IEEE Transactions on Systems,Man, and Cybernetics-Part B: Cybernetics,2011,41(4):1124-1135.
[171] Lin Z, Fang H. On asymptotic stabilizabity of linear systems with delayed input, IEEETransactions on Automatic Control,2007,52(6):998-1013.
[172] Mazenc F, Niculescu S I, Bekaik M. Backstepping for nonlinear systems with delay inthe input revisited. SIAM Journal on Control and Optimization,2011,49(6):2263-2278.
[173] Hale J.K. and Lunel S.M. Introduction to Functional Differential Equations. Springer-Verlag, New York, USA,1993.
[174] Khasminskii R. Z. Stochastic Stability of Differential Equations, Rockville, MD: Sijthoffand Noordhoff,1980.