Robust disturbance attenuation for uncertain nonlinear networked control systems

This paper considers the problem of robust disturbance attenuation for a class of uncertain nonlinear networked control systems. Takagi-Sugeno fuzzy models are firstly employed to describe the nonlinear plant. Markov processes are used to model the random network-induced delays and data packet dropouts. The Lyapunov-Razumikhin method has been used to derive such a controller for this class of nonlinear systems such that it is stochastically stabilizable with a disturbance attenuation level. Sufficient conditions for the existence of such a controller are derived in terms of the solvability of bilinear matrix inequalities. An iterative algorithm is proposed to change this non-convex problem into quasi-convex optimization problems, which can be solved effectively by available mathematical tools. The effectiveness of the proposed design methodology is verified by a numerical example.

[1]  Wei Zhang,et al.  Stability of networked control systems , 2001 .

[2]  I. Petersen,et al.  Multi-rate stabilization of multivariable discrete-time linear systems via a limited capacity communication channel , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[3]  X. Mao Stochastic Functional Differential Equations with Markovian Switching , 2004 .

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

[5]  P. Shi,et al.  Robust H/sub /spl infin// control design for uncertain fuzzy systems with Markovian jumps: an LMI approach , 2005, Proceedings of the 2005, American Control Conference, 2005..

[6]  E. Boukas,et al.  Robust Stability and Stabilizability of Markov Jump Linear Uncertain Systems with Mode-Dependent Time Delays , 2001, ACC.

[7]  Tae Woong Yoon,et al.  Proceedings of the 43rd IEEE Conference on Decision and Control , 2004 .

[8]  Rafael Castro-Linares,et al.  Trajectory tracking for non-holonomic cars: A linear approach to controlled leader-follower formation , 2010, 49th IEEE Conference on Decision and Control (CDC).

[9]  Lihua Xie,et al.  Robust control of a class of uncertain nonlinear systems , 1992 .

[10]  Sing Kiong Nguang,et al.  Static output feedback controller design for fuzzy systems: an ILMI approach , 2006, 2006 1st International Symposium on Systems and Control in Aerospace and Astronautics.

[11]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[12]  Johan Nilsson,et al.  LQG control over a Markov communication network , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[13]  P. Shi,et al.  Robust H1 control design for fuzzy singularly perturbed systems with Markovian jumps: an LMI approach , 2007 .

[14]  Y. Tipsuwan,et al.  Network-based control systems: a tutorial , 2001, IECON'01. 27th Annual Conference of the IEEE Industrial Electronics Society (Cat. No.37243).

[15]  Biao Huang,et al.  A new method for stabilization of networked control systems with random delays , 2005, Proceedings of the 2005, American Control Conference, 2005..

[16]  Linda Bushnell,et al.  Stability analysis of networked control systems , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

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

[18]  Sing Kiong Nguang,et al.  State Feedback Control of Uncertain Networked Control Systems With Random Time Delays , 2008, IEEE Trans. Autom. Control..

[19]  Nicola Elia,et al.  Stabilization of linear systems with limited information , 2001, IEEE Trans. Autom. Control..

[20]  Shengyuan Xu,et al.  Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent time delays , 2003, IEEE Trans. Autom. Control..

[21]  James Lam,et al.  Robust H∞ control of uncertain Markovian jump systems with time-delay , 2000, IEEE Trans. Autom. Control..

[22]  Sing Kiong Nguang,et al.  Robust H/sub /spl infin// control design for fuzzy singularly perturbed systems with Markovian jumps: an LMI approach , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[23]  J.P. Hespanha,et al.  Designing an observer-based controller for a network control system , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[24]  R. Srichander,et al.  Stochastic stability analysis for continuous-time fault tolerant control systems , 1993 .

[25]  Panos J. Antsaklis,et al.  Robust stability and disturbance attenuation analysis of a class of networked control systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[26]  Ilya V. Kolmanovsky,et al.  Predictive energy management of a power-split hybrid electric vehicle , 2009, 2009 American Control Conference.

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

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

[29]  Wei Zhang,et al.  Stability of networked control systems: explicit analysis of delay , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).