An H/sub /spl infin// approach to networked control

In this paper, we study the effect of a network in the feedback loop of a control system. We use a stochastic packet-loss model for the network and note that results for discrete-time linear systems with Markovian jumping parameters can be applied. We measure performance using an H/sub /spl infin// norm and compute this norm via a necessary and sufficient matrix inequality condition. We also derive necessary and sufficient linear matrix inequality (LMI) conditions for the synthesis of the H/sub /spl infin// optimal controller for a discrete-time jump system. Finally, we apply these results to study the effect of communication losses on vehicle control.

[1]  R. P. Marques,et al.  Mixed H2/H∞-control of discrete-time Markovian jump linear systems , 1998, IEEE Trans. Autom. Control..

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

[3]  J. Slaughter Quantization errors in digital control systems , 1964 .

[4]  J. Nilsson,et al.  Timing problems in real-time control systems , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[5]  Umit Ozguner,et al.  Optimal control of systems over a communication network with queues via a jump system approach , 1995, Proceedings of International Conference on Control Applications.

[6]  Ruzena Bajcsy,et al.  /spl mu/-synthesis for distributed control systems with network-induced delays , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[7]  E. O. Elliott Estimates of error rates for codes on burst-noise channels , 1963 .

[8]  Geir E. Dullerud,et al.  Networked control of distributed systems: A testbed , 2001 .

[9]  M. Tomizuka,et al.  Control issues in automated highway systems , 1994, IEEE Control Systems.

[10]  Randy H. Katz,et al.  A trace-based approach for modeling wireless channel behavior , 1996, Winter Simulation Conference.

[11]  Linda Bushnell,et al.  Asymptotic behavior of nonlinear networked control systems , 2001, IEEE Trans. Autom. Control..

[12]  J. K. Hedrick,et al.  Dynamic Coupling in Vehicles Under Automatic Control , 1994 .

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

[14]  Oswaldo L. V. Costa MIXED H 2 / H ~ CONTROL OF DISCRETE-TIME MARKOVIAN JUMP LINEAR SYSTEMS * , 1996 .

[15]  Ricardo Paulino Marques,et al.  Mixed / -Control of Discrete-Time Markovian Jump Linear Systems , 1998 .

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

[17]  Andrew Packard,et al.  The complex structured singular value , 1993, Autom..

[18]  Pravin Varaiya,et al.  A wireless token ring protocol for intelligent transportation systems , 2001, ITSC 2001. 2001 IEEE Intelligent Transportation Systems. Proceedings (Cat. No.01TH8585).

[19]  H. Chizeck,et al.  Controllability, observability and discrete-time markovian jump linear quadratic control , 1988 .

[20]  Dimitri Peaucelle,et al.  SEDUMI INTERFACE 1.02: a tool for solving LMI problems with SEDUMI , 2002, Proceedings. IEEE International Symposium on Computer Aided Control System Design.

[21]  K. Loparo,et al.  Stability and control of discrete-time jump linear systems , 1991 .

[22]  A. Willsky,et al.  Discrete-time Markovian-jump linear quadratic optimal control , 1986 .

[23]  D. Swaroop,et al.  String Stability Of Interconnected Systems: An Application To Platooning In Automated Highway Systems , 1997 .

[24]  R. P. Marques,et al.  Mixed H2/H∞-control of discrete-time Markovian jump linear systems , 1998, IEEE Trans. Autom. Control..

[25]  E. Yaz Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[26]  J. Lam,et al.  Stochastic stabilizability and H∞ control for discrete-time jump linear systems with time delay ☆ , 1999 .

[27]  Mario Sznaier,et al.  Robust Systems Theory and Applications , 1998 .

[28]  Geir E. Dullerud,et al.  Distributed control design for spatially interconnected systems , 2003, IEEE Trans. Autom. Control..

[29]  M.D. Fragoso,et al.  /spl Hscr//sub /spl infin// filtering for discrete-time linear systems with Markovian jumping parameters , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[30]  H. Chizeck,et al.  Optimal quadratic control of jump linear systems with Gaussian noise in discrete-time , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[31]  Hong Ye,et al.  Scheduling of networked control systems , 2001 .

[32]  Peter J Seiler,et al.  Analysis of communication losses in vehicle control problems , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[33]  A. Packard Gain scheduling via linear fractional transformations , 1994 .

[34]  M. Fragoso,et al.  Stability Results for Discrete-Time Linear Systems with Markovian Jumping Parameters , 1993 .

[35]  Peter J Seiler,et al.  Coordinated Control of Unmanned Aerial Vehicles , 2001 .

[36]  Stephen P. Boyd,et al.  Control of asynchronous dynamical systems with rate constraints on events , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[37]  Raja Sengupta,et al.  A bounded real lemma for jump systems , 2003, IEEE Trans. Autom. Control..

[38]  L. Ghaoui,et al.  Robust state-feedback stabilization of jump linear systems , 1996 .

[39]  D. Tilbury,et al.  Performance Evaluation of Control Networks : Ethernet , , 1999 .

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

[41]  Carlos E. de Souza,et al.  7-im Filtering for Discrete-Time Linear Systems with Markovian Jumping Parameters* , 1997 .

[42]  Datta N. Godbole,et al.  Safety and capacity analysis of automated and manual highway systems , 1998 .

[43]  A. Hassibi,et al.  Control with random communication delays via a discrete-time jump system approach , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[44]  P. Bendotti,et al.  Control of jump linear systems: application to the steam generator water level , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[45]  Gjerrit Meinsma,et al.  Unstable and nonproper weights in H∞ control , 1995, Autom..

[46]  E. Gilbert Capacity of a burst-noise channel , 1960 .

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

[48]  Anton Cervin,et al.  Distributed Wireless Control Using Bluetooth , 2001 .

[49]  José Claudio Geromel,et al.  Output feedback control of Markov jump linear systems in continuous-time , 2000, IEEE Trans. Autom. Control..

[50]  M. Steinbuch,et al.  A fast algorithm to computer the H ∞ -norm of a transfer function matrix , 1990 .

[51]  U. Ozguner,et al.  Stability of Linear Feedback Systems with Random Communication Delays , 1991, 1991 American Control Conference.

[52]  S. Shankar Sastry,et al.  HIERARCHICAL CONTROL SYSTEM SYNTHESIS FOR ROTORCRAFT-BASED UNMANNED AERIAL VEHICLES , 2000 .

[53]  El-Kébir Boukas,et al.  H/sub /spl infin// control for discrete-time linear systems with Markovian jumping parameters , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[54]  Stephen P. Boyd,et al.  A bisection method for computing the H∞ norm of a transfer matrix and related problems , 1989, Math. Control. Signals Syst..