Robust $H_{\infty}$ Control for Networked Systems With Random Packet Losses

In this paper, the robust H∞ control problem is considered for a class of networked systems with random com- munication packet losses. Because of the limited bandwidth of the channels, such random packet losses could occur, simultaneously, in the communication channels from the sensor to the controller and from the controller to the actuator. The random packet loss is assumed to obey the Bernoulli random binary distribution, and the parameter uncertainties are norm-bounded and enter into both the system and output matrices. In the presence of random packet losses, an observer-based feedback controller is designed to robustly exponentially stabilize the networked system in the sense of mean square and also achieve the prescribed H∞ disturbance-rejection-attenuation level. Both the stability-analysis and controller-synthesis problems are thoroughly investigated. It is shown that the controller-design problem under consideration is solvable if certain linear matrix inequalities (LMIs) are feasible. A simulation example is exploited to demonstrate the effectiveness of the proposed LMI approach.

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

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

[3]  Johan Nilsson,et al.  Stochastic Analysis and Control of Real-Time Systems with Random Time Delays , 1996 .

[4]  Hu Shousong,et al.  Brief Stochastic optimal control and analysis of stability of networked control systems with long delay , 2003 .

[5]  D. Hinrichsen,et al.  H∞-type control for discrete-time stochastic systems , 1999 .

[6]  Qixin Zhu,et al.  Stochastic optimal control and analysis of stability of networked control systems with long delay , 2003, Autom..

[7]  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..

[8]  Seung Ho Hong,et al.  Scheduling algorithm of data sampling times in the integrated communication and control systems , 1995, IEEE Trans. Control. Syst. Technol..

[9]  Y. Hung,et al.  Robust mixed H/sub 2//H/sub /spl infin// filtering with regional pole assignment for uncertain discrete-time systems , 2002 .

[10]  Fuwen Yang,et al.  Robust finite-horizon filtering for stochastic systems with missing measurements , 2005, IEEE Signal Processing Letters.

[11]  Raja Sengupta,et al.  An H/sub /spl infin// approach to networked control , 2005, IEEE Transactions on Automatic Control.

[12]  Dong Yue,et al.  STATE FEEDBACK CONTROLLER DESIGN OF NETWORKED CONTROL SYSTEMS WITH PARAMETER UNCERTAINTY AND STATE‐DELAY , 2006 .

[13]  I. Petersen,et al.  Robust Filtering with Missing Data and a Deterministic Description of Noise and Uncertainty , 1996 .

[14]  Long Wang,et al.  An LMI approach to networked control systems with data packet dropout and transmission delays , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[15]  D. Ho,et al.  Robust stabilization for a class of discrete-time non-linear systems via output feedback: The unified LMI approach , 2003 .

[16]  Daniel W. C. Ho,et al.  Variance-constrained control for uncertain stochastic systems with missing measurements , 2005, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[17]  Nasser E. Nahi,et al.  Optimal recursive estimation with uncertain observation , 1969, IEEE Trans. Inf. Theory.

[18]  Author Yang,et al.  Title Robust mixed H2/H∞ filtering with regional pole assignment for uncertain discrete-time systems , 2001 .

[19]  Daniel W. C. Ho,et al.  Variance-constrained filtering for uncertain stochastic systems with missing measurements , 2003, IEEE Trans. Autom. Control..

[20]  Ian R. Petersen,et al.  Model validation and state estimation for uncertain continuous-time systems with missing discrete-continuous data , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[21]  B. Azimi-Sadjadi,et al.  Stability of networked control systems in the presence of packet losses , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[22]  James Lam,et al.  Robust energy-to-peak filter design for stochastic time-delay systems , 2006, Syst. Control. Lett..

[23]  Won-jong Kim,et al.  Networked real-time control strategies dealing with stochastic time delays and packet losses , 2005, Proceedings of the 2005, American Control Conference, 2005..

[24]  Q. Han,et al.  State feedback controller design of networked control systems , 2004 .

[25]  Dong Yue,et al.  Network-based robust H ∞ control of systemswith uncertainty , 2005 .

[26]  T. Tarn,et al.  Observers for nonlinear stochastic systems , 1975, 1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes.

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

[28]  Mo-Yuen Chow,et al.  Gain adaptation of networked DC motor controllers based on QoS variations , 2003, IEEE Trans. Ind. Electron..

[29]  Graham C. Goodwin,et al.  A moving horizon approach to Networked Control system design , 2004, IEEE Transactions on Automatic Control.

[30]  Huijun Gao,et al.  New Results on Stability of Discrete-Time Systems With Time-Varying State Delay , 2007, IEEE Transactions on Automatic Control.

[31]  Qiang Ling,et al.  Soft real-time scheduling of networked control systems with dropouts governed by a Markov chain , 2003, Proceedings of the 2003 American Control Conference, 2003..