A note on stabilization via communication channel in the presence of input constraints

The problem of asymptotic stabilization of a process via communication channel under control input constraints is studied. A solution is proposed which provides encoders, decoders and controllers accomplishing global asymptotic stabilization of the closed-loop system provided that a suitable number of bits is used to encode the information generated by the process. The proposed solution shows interesting features: it employs a number of bits for encoding equal to the relative degree of the system and works in the presence of an adaptive transmission rate.

[1]  K. Loparo,et al.  Active probing for information in control systems with quantized state measurements: a minimum entropy approach , 1997, IEEE Trans. Autom. Control..

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

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

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

[5]  C. De Persis,et al.  Detecting faults from encoded information , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[6]  David Angeli,et al.  A Unifying Integral ISS Framework for Stability of Nonlinear Cascades , 2001, SIAM J. Control. Optim..

[7]  Linda Bushnell,et al.  Networks and control [Guest Editorial] , 2001 .

[8]  Alessandro Astolfi,et al.  Stabilization with positive and quantized control , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[9]  B. Achiriloaie,et al.  VI REFERENCES , 1961 .

[10]  D. Delchamps.  Extracting state information form a quantized output record , 1990 .

[11]  Graham C. Goodwin,et al.  RECEDING HORIZON LINEAR QUADRATIC CONTROL WITH FINITE INPUT CONSTRAINT SETS , 2002 .

[12]  L. Bushnell.  Networks and Control , 2001 .

[13]  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).

[14]  Eduardo Sontag.  Comments on integral variants of ISS , 1998 .

[15]  Joono Sur,et al.  State Observer for Linear Time-Invariant Systems With Quantized Output , 1998 .

[16]  Wing Shing Wong,et al.  Systems with finite communication bandwidth constraints. II. Stabilization with limited information feedback , 1999, IEEE Trans. Autom. Control..

[17]  Antonio Bicchi,et al.  On the reachability of quantized control systems , 2002, IEEE Trans. Autom. Control..

[18]  Eduardo Sontag.  Further facts about input to state stabilization , 1990 .

[19]  Eduardo Sontag.  Smooth stabilization implies coprime factorization , 1989, IEEE Transactions on Automatic Control.

[20]  Daniel Liberzon,et al.  On stabilization of linear systems with limited information , 2003, IEEE Trans. Autom. Control..

[21]  Daniel Liberzon,et al.  Hybrid feedback stabilization of systems with quantized signals , 2003, Autom..

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

[23]  L2 performance induced by feedbacks with multiple saturations , 1996 .

[24]  D. Liberzon.  STABILIZATION BY QUANTIZED STATE OR OUTPUT FEEDBACK: A HYBRID CONTROL APPROACH , 2002 .

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