Output Tracking of Stochastic High-Order Nonlinear Systems with Markovian Switching

This technical note poses and solves the output tracking problem for a class of stochastic high-order nonlinear systems with stationary Markovian switching. By introducing a II-operator and using Dynkin formula for Markovian switching systems, a switching controller is constructed to ensure that the closed-loop system has a unique solution and is bounded in probability. Also, the tracking error converges to an arbitrarily small neighborhood of zero. The efficiency of the tracking controller is demonstrated by a simulation example.

[1]  H. Chizeck,et al.  Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control , 1990 .

[2]  Guisheng Zhai,et al.  Decentralized Stabilization of Large-Scale Systems , 1998 .

[3]  Xue‐Jun Xie,et al.  State-Feedback Stabilization for High-Order Stochastic Nonlinear Systems with Stochastic Inverse Dynamics , 2007, 2007 IEEE International Conference on Control and Automation.

[4]  M. Krstić,et al.  Stochastic nonlinear stabilization—I: a backstepping design , 1997 .

[5]  E. Boukas,et al.  H∞-Control for Markovian Jumping Linear Systems with Parametric Uncertainty , 1997 .

[6]  Zhang Si-ying.  Output-feedback control of a class of high-order stochastic nonlinear systems , 2010 .

[7]  Xuerong Mao,et al.  Stochastic Differential Equations With Markovian Switching , 2006 .

[8]  Miroslav Krstic,et al.  Output-feedback stochastic nonlinear stabilization , 1999, IEEE Trans. Autom. Control..

[9]  Xue-Jun Xie,et al.  Output-Feedback Stabilization of Stochastic High-Order Nonlinear Systems under Weaker Conditions , 2011, SIAM J. Control. Optim..

[10]  Yuanwei Jing,et al.  Adaptive state-feedback stabilization for a large class of high-order stochastic nonlinear systems , 2011, Autom..

[11]  Xue-Jun Xie,et al.  Output Tracking of High-Order Stochastic Nonlinear Systems with Application to Benchmark Mechanical System , 2010, IEEE Transactions on Automatic Control.

[12]  Xue-Jun Xie,et al.  Inverse optimal stabilization for stochastic nonlinear systems whose linearizations are not stabilizable , 2009, Autom..

[13]  Gopal K. Basak,et al.  Stability of a Random diffusion with linear drift , 1996 .

[14]  Yongduan Song,et al.  ${\cal H}_{\infty}$ Model Reduction of Takagi–Sugeno Fuzzy Stochastic Systems , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[15]  Ligang Wu,et al.  Sliding mode control with bounded L2 gain performance of Markovian jump singular time-delay systems , 2012, Autom..

[16]  Yuanwei Jing,et al.  State feedback control of a class of high‐order stochastic nonlinear systems , 2012 .

[17]  Yuanqing Xia,et al.  Control for discrete singular hybrid systems , 2008, Autom..

[18]  H. Deng,et al.  Stochastic Nonlinear Stabilization|part I: a Backstepping Design Submitted to Systems and Control Letters , 1997 .

[19]  Yuanqing Xia,et al.  Stability and stabilization of continuous-time singular hybrid systems , 2009, Autom..

[20]  Takahiro Yamaguchi,et al.  STOCHASTIC MOTION OF NONLINEAR SYSTEMS OF VAN DER POL-MATHIEU TYPE , 2012 .

[21]  Yuanwei Jing,et al.  Decentralised stabilisation of a class of large-scale high-order stochastic non-linear systems , 2010 .

[22]  Xiaohua Liu,et al.  Further results on adaptive state-feedback stabilization for stochastic high-order nonlinear systems , 2012, Autom..

[23]  Xuerong Mao,et al.  Robust stability and controllability of stochastic differential delay equations with Markovian switching , 2004, Autom..

[24]  X. Mao.  Stability of stochastic differential equations with Markovian switching , 1999 .

[25]  Xinjiang Wei,et al.  Decentralised output-feedback control for high-order stochastic non-linear systems , 2012 .

[26]  Guo-Ping Liu,et al.  Delay-dependent stability for discrete systems with large delay sequence based on switching techniques , 2008, Autom..

[27]  Annie Cuyt,et al.  Nonlinear Methods in Numerical Analysis , 1987 .

[28]  Yuanqing Xia,et al.  On designing of sliding-mode control for stochastic jump systems , 2006, IEEE Transactions on Automatic Control.

[29]  Arunabha Bagchi,et al.  Adaptive filtering for stochastic risk premia in bond market , 2012 .

[30]  Peng Shi,et al.  Adaptive Tracking for Stochastic Nonlinear Systems With Markovian Switching $ $ , 2010, IEEE Transactions on Automatic Control.

[31]  Wei Lin,et al.  Adaptive control of nonlinearly parameterized systems: the smooth feedback case , 2002, IEEE Trans. Autom. Control..

[32]  Xue‐Jun Xie,et al.  Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching , 2008, CCC 2008.

[33]  William B. Jones,et al.  A survey of truncation error analysis for Padé and continued fraction approximants , 1993 .