Adaptive fuzzy tracking control for stochastic nonlinear systems with unknown time-varying delays

An adaptive fuzzy controller is presented for a class of stochastic nonlinear systems.An quadratic function is constructed to give the condition of the stability of systems.The scheme guarantees the stability of closed-loop system in the mean square sense.The drawback of the quartic moment approach is overcome and the method is simplified. This paper addresses the problem of adaptive tracking control for a class of stochastic strict-feedback nonlinear time-varying delays systems using fuzzy logic systems (FLS). In this paper, quadratic functions are used as Lyapunov functions to analyze the stability of systems, other than the fourth moment approach proposed by H. Deng and M. Krstic, and the hyperbolic tangent functions are introduced to deal with the Hessian terms. This approach overcomes the drawback of the traditional quadratic moment approach and reduce the complexity of design procedure and controller. Based on the backstepping technique, the appropriate Lyapunov-Krasovskii functionals and the FLS, the adaptive fuzzy controller is well designed. The proposed adaptive fuzzy controller guarantees that all the signals in the closed-loop system are bounded in probability and the tracking error can converge to a small residual set around the origin in the mean square sense.

[1]  Shaocheng Tong,et al.  Adaptive fuzzy backstepping output feedback control for a class of uncertain stochastic nonlinear system in pure-feedback form , 2013, Neurocomputing.

[2]  Jinde Cao,et al.  Global robust stability of interval cellular neural networks with time-varying delays , 2005 .

[3]  Shaocheng Tong,et al.  Observer-based adaptive fuzzy decentralized control for stochastic large-scale nonlinear systems with unknown dead-zones , 2014, Inf. Sci..

[4]  Junwei Lu,et al.  Tuning functions‐based robust adaptive tracking control of a class of nonlinear systems with time delays , 2012 .

[5]  Li-Xin Wang,et al.  Adaptive fuzzy systems and control - design and stability analysis , 1994 .

[6]  Xin-Ping Guan,et al.  Adaptive Fuzzy Output-Feedback Controller Design for Nonlinear Time-Delay Systems With Unknown Control Direction , 2009, IEEE Trans. Syst. Man Cybern. Part B.

[7]  Shaocheng Tong,et al.  Observer-Based Adaptive Fuzzy Backstepping Control for a Class of Stochastic Nonlinear Strict-Feedback Systems , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[8]  M. Krstić,et al.  Stochastic nonlinear stabilization—II: inverse optimality , 1997 .

[9]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .

[10]  Bing Chen,et al.  Adaptive fuzzy tracking control of nonlinear time-delay systems with unknown virtual control coefficients , 2008, Inf. Sci..

[11]  Wei Lin,et al.  Adaptive control of nonlinearly parameterized systems: a nonsmooth feedback framework , 2002, IEEE Trans. Autom. Control..

[12]  Shaocheng Tong,et al.  Adaptive fuzzy decentralized output feedback control for stochastic nonlinear large-scale systems , 2012, Neurocomputing.

[13]  Zhaoxu Yu,et al.  Adaptive neural control for a class of non-affine stochastic non-linear systems with time-varying delay: A Razumikhin-Nussbaum method , 2012 .

[14]  X. Mao.  LaSalle-Type Theorems for Stochastic Differential Delay Equations , 1999 .

[15]  R. Khasminskii.  Stochastic Stability of Differential Equations , 1980 .

[16]  Licheng Jiao,et al.  Adaptive NN Backstepping Output-Feedback Control for Stochastic Nonlinear Strict-Feedback Systems With Time-Varying Delays , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[17]  Bing Chen,et al.  Adaptive neural tracking control for stochastic nonlinear strict-feedback systems with unknown input saturation , 2014, Inf. Sci..

[18]  Miroslav Krstic,et al.  Stabilization of Nonlinear Uncertain Systems , 1998 .

[19]  Shumin Fei,et al.  Adaptive Fuzzy Tracking Control of a Class of Stochastic Nonlinear Systems with Unknown Dead-Zone Input , 2008 .

[20]  Zhong-Ping Jiang,et al.  Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems , 2007, Autom..

[21]  Zhaoxu Yu,et al.  Neural-network-based output-feedback adaptive dynamic surface control for a class of stochastic nonlinear time-delay systems with unknown control directions , 2014, Neurocomputing.

[22]  Hai-Bo Ji,et al.  Adaptive output-feedback tracking of stochastic nonlinear systems , 2006, IEEE Trans. Autom. Control..

[23]  Xue‐Jun Xie,et al.  State‐feedback stabilization for high‐order stochastic nonlinear systems with stochastic inverse dynamics , 2007 .

[24]  Bing Chen,et al.  Adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear time-delay systems , 2008, Fuzzy Sets Syst..

[25]  Junmi Li,et al.  Adaptive NN output-feedback stabilization for a class of stochastic nonlinear strict-feedback systems. , 2009, ISA transactions.

[26]  Miroslav Krstic,et al.  Stabilization of stochastic nonlinear systems driven by noise of unknown covariance , 2001, IEEE Trans. Autom. Control..

[27]  T. Başar,et al.  Adaptive controller design for tracking and disturbance attenuation in parametric strict-feedback nonlinear systems , 1998, IEEE Trans. Autom. Control..

[28]  Chung-Shi Tseng,et al.  H Fuzzy Control Design for Nonlinear Stochastic Fuzzy Systems , 2007 .

[29]  Tamer Basar,et al.  Risk-sensitive adaptive trackers for strict-feedback systems with output measurements , 2002, IEEE Trans. Autom. Control..

[30]  Ji-Feng Zhang,et al.  Practical Output-Feedback Risk-Sensitive Control for Stochastic Nonlinear Systems with Stable Zero-Dynamics , 2006, SIAM J. Control. Optim..

[31]  Wenwu Yu,et al.  Global robust stability of neural networks with time varying delays , 2007 .

[32]  Shengyuan Xu,et al.  Asymptotic Tracking Control of Uncertain Nonlinear Systems With Unknown Actuator Nonlinearity , 2014, IEEE Transactions on Automatic Control.

[33]  Yungang Liu,et al.  Output feedback control design for strict-feedback stochastic nonlinear systems under a risk-sensitive cost , 2003, IEEE Trans. Autom. Control..

[34]  Shuzhi Sam Ge,et al.  Adaptive neural control of MIMO nonlinear state time-varying delay systems with unknown dead-zones and gain signs , 2007, Autom..

[35]  Jie Tian,et al.  Adaptive state-feedback stabilization of high-order stochastic systems with nonlinear parameterization , 2009, Autom..

[36]  Peng Shi,et al.  Robust backstepping control for a class of time delayed systems , 2005, IEEE Transactions on Automatic Control.

[37]  Keng Peng Tee,et al.  Approximation-based control of nonlinear MIMO time-delay systems , 2007, Autom..

[38]  Shuzhi Sam Ge,et al.  Adaptive output-feedback control for a class of uncertain stochastic non-linear systems with time delays , 2008, Int. J. Control.