Nonfragile Gain-Scheduled Control for Discrete-Time Stochastic Systems with Randomly Occurring Sensor Saturations

This paper is devoted to tackling the control problem for a class of discrete-time stochastic systems with randomly occurring sensor saturations. The considered sensor saturation phenomenon is assumed to occur in a random way based on the time-varying Bernoulli distribution with measurable probability in real time. The aim of the paper is to design a nonfragile gain-scheduled controller with probability-dependent gains which can be achieved by solving a convex optimization problem via semidefinite programming method. Subsequently, a new kind of probability-dependent Lyapunov functional is proposed in order to derive the controller with less conservatism. Finally, an illustrative example will demonstrate the effectiveness of our designed procedures.

[1]  Zidong Wang,et al.  Global asymptotic stability of uncertain stochastic bi-directional associative memory networks with discrete and distributed delays , 2009, Math. Comput. Simul..

[2]  Zongli Lin,et al.  Set invariance analysis and gain-scheduling control for LPV systems subject to actuator saturation , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[3]  Bo Shen,et al.  Recent Advances on Filtering and Control for Nonlinear Stochastic Complex Systems with Incomplete Information: A Survey , 2012 .

[4]  Maozhen Li,et al.  Probability-Dependent Gain-Scheduled Filtering for Stochastic Systems With Missing Measurements , 2011, IEEE Transactions on Circuits and Systems II: Express Briefs.

[5]  Fuwen Yang,et al.  Robust H-infinity filtering for stochastic time-delay systems with missing measurements , 2006 .

[6]  Jianbin Qiu,et al.  Fuzzy-Model-Based Piecewise ${\mathscr H}_{\infty }$ Static-Output-Feedback Controller Design for Networked Nonlinear Systems , 2010, IEEE Transactions on Fuzzy Systems.

[7]  Zidong Wang,et al.  $H_{\infty}$ State Estimation for Discrete-Time Complex Networks With Randomly Occurring Sensor Saturations and Randomly Varying Sensor Delays , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[8]  Jun Hu,et al.  Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements , 2012, Autom..

[9]  Robert E. Skelton,et al.  Static output feedback controllers: stability and convexity , 1998, IEEE Trans. Autom. Control..

[10]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[11]  P. Dorato,et al.  Non-fragile controller design: an overview , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[12]  Wilson J. Rugh,et al.  Research on gain scheduling , 2000, Autom..

[13]  P. Apkarian,et al.  Advanced gain-scheduling techniques for uncertain systems , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[14]  Fuwen Yang,et al.  Robust H/sub /spl infin// filtering for stochastic time-delay systems with missing measurements , 2006, IEEE Transactions on Signal Processing.

[15]  Jun Hu,et al.  Quantised recursive filtering for a class of nonlinear systems with multiplicative noises and missing measurements , 2013, Int. J. Control.

[16]  Zidong Wang,et al.  Probability‐dependent gain‐scheduled control for discrete stochastic delayed systems with randomly occurring nonlinearities , 2013 .

[17]  Guang-Hong Yang,et al.  Non-fragile Hinfinity filter design for linear continuous-time systems , 2008, Autom..

[18]  James Lam,et al.  Static Output Feedback Stabilization: An ILMI Approach , 1998, Autom..

[19]  Jun Hu,et al.  Gain-Constrained Recursive Filtering With Stochastic Nonlinearities and Probabilistic Sensor Delays , 2013, IEEE Transactions on Signal Processing.

[20]  Fuwen Yang,et al.  H∞ control for networked systems with random communication delays , 2006, IEEE Trans. Autom. Control..

[21]  Zidong Wang,et al.  H∞ filtering with randomly occurring sensor saturations and missing measurements , 2012, Autom..

[22]  Guoliang Wei,et al.  Probability-Dependent Static Output Feedback Control for Discrete-Time Nonlinear Stochastic Systems with Missing Measurements , 2012 .

[23]  H. Shu,et al.  H∞ analysis of nonlinear stochastic time-delay systems , 2005 .

[24]  P. Dorato,et al.  Static output feedback: a survey , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[25]  Indra Narayan Kar.  Design of static output feedback controller for uncertain systems , 1999, Autom..

[26]  Y. Jia,et al.  Non-fragile dynamic output feedback control for linear systems with time-varying delay , 2009 .

[27]  Jun Hu,et al.  H ∞  sliding mode observer design for a class of nonlinear discrete time‐delay systems: A delay‐fractioning approach , 2012 .

[28]  Jun Hu,et al.  Robust Sliding Mode Control for Discrete Stochastic Systems With Mixed Time Delays, Randomly Occurring Uncertainties, and Randomly Occurring Nonlinearities , 2012, IEEE Transactions on Industrial Electronics.

[29]  Ju H. Park.  Robust non-fragile control for uncertain discrete-delay large-scale systems with a class of controller gain variations , 2004, Appl. Math. Comput..