On the design of control systems over unreliable channels

This paper studies LTI one-degree-of-freedom networked control architectures built around LTI SISO plants. The feedback path comprises an unreliable channel that drops data in an i.i.d. fashion. We extend known results to show that there exists a second order moments equivalence between the situation examined and an auxiliary feedback loop where the unreliable channel has been replaced by an additive i.i.d. noise channel that has an equality signal-to-noise ratio constraint. We then use these insights to design optimal controllers. We also establish a necessary and sufficient condition on the successful transmission probability that allows for the design of a controller that guarantees MSS in the considered setup. Our proposal does not require packet arrival acknowledgements. Thus, our results give necessary and sufficient conditions for MSS in an output-feedback control architecture with UDP-like protocols.

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

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

[3]  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).

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

[5]  Graham C. Goodwin,et al.  Optimal controller design for networked control systems , 2008 .

[6]  Evanghelos Zafiriou,et al.  Robust process control , 1987 .

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

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

[9]  L. Qiu,et al.  Tracking performance limitations in LTI multivariable discrete-time systems , 2002 .

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

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

[12]  Joe Brewer,et al.  Kronecker products and matrix calculus in system theory , 1978 .

[13]  Frank Kozin,et al.  A survey of stability of stochastic systems , 1969, Autom..

[14]  Y. Tipsuwan,et al.  Control methodologies in networked control systems , 2003 .

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

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

[17]  Torsten Söderström,et al.  Discrete-time Stochastic Systems , 2002 .

[18]  Robin J. Evans,et al.  Feedback Control Under Data Rate Constraints: An Overview , 2007, Proceedings of the IEEE.

[19]  William H. Press,et al.  Numerical Recipes in FORTRAN - The Art of Scientific Computing, 2nd Edition , 1987 .

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

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

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

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

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

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

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

[27]  Cristian Oara.  Constructive solutions to spectral and inner-outer factorizations with respect to the disk , 2005, Autom..

[28]  Qiang Ling,et al.  Stability and performance of control systems with limited feedback information , 2005 .

[29]  C. Oar.  Constructive solutions to spectral and inner-outer factorizations with respect to the disk , 2005 .

[30]  Babak Hassibi,et al.  On LQG control across a stochastic packet-dropping link , 2005, Proceedings of the 2005, American Control Conference, 2005..