Global output feedback stabilisation for a class of upper triangular stochastic nonlinear systems

This paper investigates the problem of global output feedback stabilisation for a class of upper triangular stochastic nonlinear systems which are neither necessarily feedback linearisable nor affine in the control input. Based on the adding of a power integrator technique and homogeneous domination approach, an output feedback controller is explicitly constructed to ensure that the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability. A simulation example is provided to demonstrate the effectiveness of the design scheme.

[1]  C. Qian,et al.  A Generalized Framework for Global Output Feedback Stabilization of Genuinely Nonlinear Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[2]  T. Basar,et al.  Backstepping controller design for nonlinear stochastic systems under a risk-sensitive cost criterion , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[3]  Junyong Zhai,et al.  Output feedback control for a class of stochastic high‐order nonlinear systems with time‐varying delays , 2014 .

[4]  Junyong Zhai,et al.  Global practical tracking control for a class of uncertain non-linear systems [Brief Paper] , 2011 .

[5]  P. Florchinger.  Lyapunov-like techniques for stochastic stability , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[6]  Xue-Jun Xie,et al.  Output-feedback Stabilization for Stochastic High-order Nonlinear Systems with a Ratio of Odd Integers Power: Output-feedback Stabilization for Stochastic High-order Nonlinear Systems with a Ratio of Odd Integers Power , 2010 .

[7]  Xue-Jun Xie,et al.  Output-feedback Stabilization for Stochastic High-order Nonlinear Systems with a Ratio of Odd Integers Power , 2010 .

[8]  A. Isidori.  Nonlinear Control Systems , 1985 .

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

[10]  Alessandro Astolfi,et al.  High gain observers with updated gain and homogeneous correction terms , 2009, Autom..

[11]  Chunjiang Qian,et al.  Global Output Feedback Stabilization of a Class of Nonlinear Systems via Linear Sampled-Data Control , 2012, IEEE Transactions on Automatic Control.

[12]  Guodong Zhao,et al.  A homogeneous domination approach to state feedback of stochastic high-order feedforward nonlinear systems , 2013, Int. J. Control.

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

[14]  Zhong-Ping Jiang,et al.  Global Output-Feedback Stabilization for a Class of Stochastic Non-Minimum-Phase Nonlinear Systems , 2007, 2007 IEEE International Conference on Control Applications.

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

[16]  Xue-Jun Xie,et al.  Output-feedback control of a class of high-order stochastic nonlinear systems , 2009, Int. J. Control.

[17]  M. Kawski.  Stability and nilpotent approximations , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

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

[19]  Wei Lin,et al.  A continuous feedback approach to global strong stabilization of nonlinear systems , 2001, IEEE Trans. Autom. Control..

[20]  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).

[21]  L. Rosier.  Homogeneous Lyapunov function for homogeneous continuous vector field , 1992 .

[22]  A. Bacciotti,et al.  Liapunov functions and stability in control theory , 2001 .

[23]  Ruth J. Williams,et al.  Stabilization of stochastic nonlinear systems driven by noise of unknown covariance , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[24]  Alessandro Astolfi,et al.  Homogeneous Approximation, Recursive Observer Design, and Output Feedback , 2008, SIAM J. Control. Optim..

[25]  Junyong Zhai,et al.  Global control of nonlinear systems with uncertain output function using homogeneous domination approach , 2012 .

[26]  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.

[27]  W. Dayawansa,et al.  Global stabilization by output feedback: examples and counterexamples , 1994 .

[28]  P. Florchinger.  A universal formula for the stabilization of control stochastic differential equations , 1993 .

[29]  Eduardo Sontag.  A universal construction of Artstein's theorem on nonlinear stabilization , 1989 .

[30]  Chunjiang Qian,et al.  A homogeneous domination approach for global output feedback stabilization of a class of nonlinear systems , 2005, Proceedings of the 2005, American Control Conference, 2005..

[31]  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).

[32]  J. Tsinias.  A theorem on global stabilization of nonlinear systems by linear feedback , 1991 .

[33]  Yuanwei Jing,et al.  Output-feedback stabilization for stochastic nonlinear systems whose linearizations are not stabilizable , 2010, Autom..