Analysis and synthesis of networked control systems: Topological entropy, observability, robustness and optimal control

This paper extends the concept of topological to the case of uncertain dynamical systems. We address problems of observability and optimal control via limited capacity digital communication channels. The main results are given in terms of inequalities between date rate of the communication channel and topological entropy of the open-loop system. Topological entropy is calculated for some classes of uncertain dynamical systems.

[1]  Robin J. Evans,et al.  Topological feedback entropy and Nonlinear stabilization , 2004, IEEE Transactions on Automatic Control.

[2]  R. Evans,et al.  Stabilization with data-rate-limited feedback: tightest attainable bounds , 2000 .

[3]  George A. Perdikaris.  Computer Controlled Systems , 1991 .

[4]  Daniel Liberzon,et al.  Quantized feedback stabilization of linear systems , 2000, IEEE Trans. Autom. Control..

[5]  Ian R. Petersen,et al.  Robust Control Design Using H-infinity Methods , 2000 .

[6]  Roy L. Adler,et al.  Topological entropy , 2008, Scholarpedia.

[7]  Ian R. Petersen,et al.  Nonlinear versus linear control in the absolute stabilizability of uncertain systems with structured uncertainty , 1995, IEEE Trans. Autom. Control..

[8]  Naim A. Kheir,et al.  Control system design , 2001, Autom..

[9]  Daniel J. Stilwell,et al.  Platoons of underwater vehicles , 2000 .

[10]  A.S. Matveev,et al.  An analogue of Shannon information theory for networked control systems: State estimation via a noisy discrete channel , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[11]  Ian R. Petersen,et al.  A connection between H ∞ control and the absolute stabilizability of uncertain systems , 1994 .

[12]  R. Evans,et al.  Mean square stabilisability of stochastic linear systems with data rate constraints , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[13]  Andrey V. Savkin,et al.  An analogue of Shannon information theory for networked control systems. Stabilization via a noisy discrete channel , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[14]  K. Narendra,et al.  Frequency Domain Criteria for Absolute Stability , 1973 .

[15]  Andrey V. Savkin,et al.  The problem of LQG optimal control via a limited capacity communication channel , 2004, Syst. Control. Lett..

[16]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[17]  M. Pollicott,et al.  Dynamical Systems and Ergodic Theory , 1998 .

[18]  Sekhar Tatikonda,et al.  Control under communication constraints , 2004, IEEE Transactions on Automatic Control.

[19]  Lemma Vi,et al.  Set-Valued State Estimation via a Limited Capacity Communication Channel , 2003 .

[20]  Andrey V. Savkin,et al.  Multirate Stabilization of Linear Multiple Sensor Systems via Limited Capacity Communication Channels , 2005, SIAM J. Control. Optim..

[21]  W. Moran,et al.  Topological feedback entropy for nonlinear systems , 2004, 2004 5th Asian Control Conference (IEEE Cat. No.04EX904).

[22]  R. Brockett,et al.  Systems with finite communication bandwidth constraints. I. State estimation problems , 1997, IEEE Trans. Autom. Control..

[23]  R. Adler,et al.  Entropy, a complete metric invariant for automorphisms of the torus. , 1967, Proceedings of the National Academy of Sciences of the United States of America.

[24]  Ian R. Petersen,et al.  Robust Kalman Filtering for Signals and Systems with Large Uncertainties , 1999 .

[25]  A.S. Matveev,et al.  Stabilization of multisensor networked control systems with communication constraints , 2004, 2004 5th Asian Control Conference (IEEE Cat. No.04EX904).

[26]  Bruce A. Francis,et al.  Limited Data Rate in Control Systems with Networks , 2002 .

[27]  Ian R. Petersen,et al.  Set-valued state estimation via a limited capacity communication channel , 2003, IEEE Trans. Autom. Control..