Globally asymptotic stabilization of stochastic nonlinear systems in strict-feedback form

Abstract In this paper, we study the problem of globally asymptotic stabilization for a class of stochastic nonlinear systems. Without requiring the condition that the coefficients are smooth functions, this paper is a first try to apply the backstepping control design method to prove the globally asymptotic stability in probability of stochastic nonlinear systems in strict-feedback form. A continuous control law is constructed by a novel systematic design algorithm. Finally, we provide an example to show the effectiveness of the theoretical results.

[1]  Peng Shi,et al.  Adaptive tracking control for switched stochastic nonlinear systems with unknown actuator dead-zone , 2015, Autom..

[2]  Huijun Gao,et al.  Distributed Filtering for a Class of Time-Varying Systems Over Sensor Networks With Quantization Errors and Successive Packet Dropouts , 2012, IEEE Transactions on Signal Processing.

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

[4]  L. Ghaoui,et al.  LMI optimization for nonstandard Riccati equations arising in stochastic control , 1996, IEEE Trans. Autom. Control..

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

[6]  H. Schurz.  Stability, stationarity, and boundedness of some implicit numerical methods for stochastic differential equations and applications , 1997 .

[7]  Zhihong Man,et al.  Finite-time stabilization of stochastic nonlinear systems in strict-feedback form , 2013, Autom..

[8]  Huijun Gao,et al.  Finite-horizon reliable control with randomly occurring uncertainties and nonlinearities subject to output quantization , 2015, Autom..

[9]  Xuerong Mao,et al.  Stability in distribution of stochastic differential delay equations with Markovian switching , 2003, Syst. Control. Lett..

[10]  Xuerong Mao,et al.  Stochastic Versions of the LaSalle Theorem , 1999 .

[11]  Xuerong Mao,et al.  Stochastic differential equations and their applications , 1997 .

[12]  Lirong Huang.  Stochastic stabilization and destabilization of nonlinear differential equations , 2013, Syst. Control. Lett..

[13]  X. Mao,et al.  A note on the LaSalle-type theorems for stochastic differential delay equations , 2002 .

[14]  Shengyuan Xu,et al.  Stabilisation of stochastic systems with optimal decay rate , 2008 .

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

[16]  Quanxin Zhu,et al.  pth Moment exponential stability of impulsive stochastic functional differential equations with Markovian switching , 2014, J. Frankl. Inst..

[17]  H. Kushner.  Stochastic Stability and Control , 2012 .

[18]  Oleksiy A. Ignatyev,et al.  Barbashin-Krasovskii theorem for stochastic differential equations , 2010 .

[19]  Yi Shen,et al.  Stability and boundedness of nonlinear hybrid stochastic differential delay equations , 2013, Syst. Control. Lett..

[20]  X. Mao,et al.  Exponential Stability of Stochastic Di erential Equations , 1994 .

[21]  Bor-Sen Chen,et al.  On stabilizability and exact observability of stochastic systems with their applications , 2023, Autom..

[22]  T. Başar,et al.  Backstepping Controller Design for Nonlinear Stochastic Systems Under a Risk-Sensitive Cost Criterion , 1999 .

[23]  Huijun Gao,et al.  Finite-horizon estimation of randomly occurring faults for a class of nonlinear time-varying systems , 2014, Autom..

[24]  B. Øksendal.  Stochastic Differential Equations , 1985 .

[25]  Xuerong Mao,et al.  Stabilization of continuous-time hybrid stochastic differential equations by discrete-time feedback control , 2013, Autom..

[26]  Bing Li,et al.  Stability analysis for impulsive stochastic delay differential equations with Markovian switching , 2013, J. Frankl. Inst..

[27]  Quanxin Zhu,et al.  Exponential stability of impulsive nonlinear stochastic differential equations with mixed delays , 2011 .

[28]  Nguyen Huu Du,et al.  On stability in distribution of stochastic differential delay equations with Markovian switching , 2014, Syst. Control. Lett..

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