Control of LTI plants over erasure channels

This paper studies linear time-invariant (LTI) control architectures for LTI plants when communication takes place over a scalar erasure channel. Assuming i.i.d. data dropouts, we first show that such a channel is equivalent, in a second order moment sense, to an additive white noise channel subject to an instantaneous signal-to-noise ratio constraint. This key result is then exploited in two ways: First, we use it to characterize the set of all LTI controllers that achieve mean square stability in control architectures closed over scalar erasure channels. Second, we use it to show that the optimal design of LTI controllers over scalar erasure channels can be carried out by using tools from standard quadratic optimal control theory. We finally apply our results to the dynamic output feedback control of LTI single-input single-output (SISO) plants subject to data dropouts. In this case, we are able to establish closed form necessary and sufficient conditions on the minimal successful transmission probability that allows one to design mean square stabilizing controllers.

[1]  Eduardo I. Silva,et al.  A unified framework for the analysis and design of networked control systems , 2009 .

[2]  Christoforos N. Hadjicostis,et al.  Feedback control utilizing packet dropping network links , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[3]  Alejandro J. Rojas.  Comments on "Feedback stabilization over signal-to-noise ratio constrained channels , 2009, IEEE Trans. Autom. Control..

[4]  Andrey V. Savkin,et al.  Comments on "Control over noisy channels" and relevant negative results , 2005, IEEE Trans. Autom. Control..

[5]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[6]  Richard M. Murray,et al.  Optimal LQG control across packet-dropping links , 2007, Syst. Control. Lett..

[7]  Sekhar Tatikonda,et al.  Control over noisy channels , 2004, IEEE Transactions on Automatic Control.

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

[9]  Johan Nilsson,et al.  Real-Time Control Systems with Delays , 1998 .

[10]  N. Elia,et al.  Limitations of linear remote control over packet drop networks , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[11]  Graham C. Goodwin,et al.  Control system design subject to SNR constraints , 2010, Autom..

[12]  Shinji Hara,et al.  A subband coding approach to control under limited data rates and message losses , 2008, Autom..

[13]  Panos J. Antsaklis,et al.  Special Issue on Technology of Networked Control Systems , 2007 .

[14]  Graham C. Goodwin,et al.  On the design of control systems over unreliable channels , 2009, 2009 European Control Conference (ECC).

[15]  Tamer Basar,et al.  Optimal control of LTI systems over unreliable communication links , 2006, Autom..

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

[17]  R. P. Marques,et al.  Discrete-Time Markov Jump Linear Systems , 2004, IEEE Transactions on Automatic Control.

[18]  Bruno Sinopoli,et al.  Foundations of Control and Estimation Over Lossy Networks , 2007, Proceedings of the IEEE.

[19]  Bruno Sinopoli,et al.  Optimal linear LQG control over lossy networks without packet acknowledgment , 2008 .

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

[21]  Nicola Elia,et al.  Remote stabilization over fading channels , 2005, Syst. Control. Lett..

[22]  Richard H. Middleton,et al.  Feedback stabilization over signal-to-noise ratio constrained channels , 2007, Proceedings of the 2004 American Control Conference.

[23]  Vijay Gupta,et al.  On Stability in the Presence of Analog Erasure Channel Between the Controller and the Actuator , 2010, IEEE Transactions on Automatic Control.

[24]  João Pedro Hespanha,et al.  A Survey of Recent Results in Networked Control Systems , 2007, Proceedings of the IEEE.

[25]  John S. Baras,et al.  Optimal Output Feedback Control Using Two Remote Sensors Over Erasure Channels , 2009, IEEE Transactions on Automatic Control.

[26]  Claudio De Persis,et al.  Proceedings of the 41st IEEE Conference on Decision and Control , 2002 .

[27]  Qiang Ling,et al.  Power spectral analysis of networked control systems with data dropouts , 2004, IEEE Transactions on Automatic Control.

[28]  Alim P. C. Gonçalves,et al.  Dynamic Output Feedback Control of Discrete-Time Markov Jump Linear Systems through Linear Matrix Inequalities , 2009, SIAM J. Control. Optim..