Optimal LQG control across packet-dropping links

We examine two special cases of the problem of optimal linear quadratic Gaussian control of a system whose state is being measured by sensors that communicate with the controller over packet-dropping links. We pose the problem as an information transmission problem. Using a separation principle, we decompose the problem into a standard LQR state-feedback controller design, along with an optimal encoder–decoder design for propagating and using the information across the unreliable links. Our design is optimal among all causal algorithms for any arbitrary packet-drop pattern. Further, the solution is appealing from a practical point of view because it can be implemented as a small modification of an existing LQG control design.

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

[2]  Anant Sahai,et al.  Anytime information theory , 2001 .

[3]  Sumit Roy,et al.  Decentralized structures for parallel Kalman filtering , 1988 .

[4]  D. Delchamps Stabilizing a linear system with quantized state feedback , 1990 .

[5]  Babak Hassibi,et al.  Indefinite-Quadratic Estimation And Control , 1987 .

[6]  Yaakov Bar-Shalom,et al.  The Effect of the Common Process Noise on the Two-Sensor Fused-Track Covariance , 1986, IEEE Transactions on Aerospace and Electronic Systems.

[7]  Robin J. Evans,et al.  Stabilizability of Stochastic Linear Systems with Finite Feedback Data Rates , 2004, SIAM J. Control. Optim..

[8]  John B. Moore,et al.  Hidden Markov Models: Estimation and Control , 1994 .

[9]  Panos J. Antsaklis,et al.  Guest Editorial Special Issue on Networked Control Systems , 2004, IEEE Trans. Autom. Control..

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

[11]  Kannan Ramchandran,et al.  On rate-constrained distributed estimation in unreliable sensor networks , 2005, IEEE Journal on Selected Areas in Communications.

[12]  Y. Bar-Shalom,et al.  On optimal track-to-track fusion , 1997, IEEE Transactions on Aerospace and Electronic Systems.

[13]  Qiang Ling,et al.  Soft real-time scheduling of networked control systems with dropouts governed by a Markov chain , 2003, Proceedings of the 2003 American Control Conference, 2003..

[14]  N. Tsai,et al.  Stochastic optimal control under randomly varying distributed delays , 1997 .

[15]  Bruce A. Francis,et al.  Quadratic stabilization of sampled-data systems with quantization , 2003, Autom..

[16]  Richard M. Murray,et al.  On the control of jump linear Markov systems with Markov state estimation , 2003, Proceedings of the 2003 American Control Conference, 2003..

[17]  D. Sworder,et al.  Feedback control of a class of linear discrete systems with jump parameters and quadratic cost criteria , 1975 .

[18]  C. Chang,et al.  Kalman filter algorithms for a multi-sensor system , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

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

[20]  Jason Speyer,et al.  Computation and transmission requirements for a decentralized linear-quadratic-Gaussian control problem , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[21]  Saleem A. Kassam,et al.  Finite-state Markov model for Rayleigh fading channels , 1999, IEEE Trans. Commun..

[22]  Bruno Sinopoli,et al.  LQG CONTROL WITH MISSING OBSERVATION AND CONTROL PACKETS , 2005 .

[23]  Y. Bar-Shalom On the track-to-track correlation problem , 1981 .

[24]  Richard M. Murray,et al.  On a stochastic sensor selection algorithm with applications in sensor scheduling and sensor coverage , 2006, Autom..

[25]  Michael Athans,et al.  Proceedings of the MIT/ONR Workshop on Distributed Communication and Decision Problems Motivated by Naval C3 Systems (2nd). Held in Monterey, California on 16-27 July 1979. Volume 2 , 1980 .

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

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

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

[29]  J. Hespanha,et al.  Towards the Control of Linear Systems with Minimum Bit-Rate , 2002 .

[30]  B. Azimi-Sadjadi,et al.  Stability of networked control systems in the presence of packet losses , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[31]  H. F. Durrant-Whyte,et al.  Fully decentralised algorithm for multisensor Kalman filtering , 1991 .

[32]  R.M. Murray,et al.  The Caltech Multi-Vehicle Wireless Testbed , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[33]  K. Poolla,et al.  Time varying optimal control with packet losses , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

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

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

[36]  Special Issue on Networked Control Systems , .

[37]  S. Dey,et al.  Infimum data rates for stabilising Markov jump linear systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[38]  George C. Verghese,et al.  A scattering framework for decentralized estimation problems , 1983, Autom..

[39]  Peter Lancaster,et al.  The theory of matrices , 1969 .

[40]  Tamer Basar,et al.  Optimal control of dynamical systems over unreliable communication links , 2004 .

[41]  Qiang Ling,et al.  Optimal dropout compensation in networked control systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[42]  Bruno Sinopoli,et al.  Kalman filtering with intermittent observations , 2004, IEEE Transactions on Automatic Control.

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

[44]  Michael D. Lemmon,et al.  Robust performance of soft real-time networked control systems with data dropouts , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[45]  H. Witsenhausen Separation of estimation and control for discrete time systems , 1971 .

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

[47]  N. A. Carlson Federated square root filter for decentralized parallel processors , 1990 .

[48]  Kuo-Chu Chang,et al.  Information Fusion in Distributed Sensor Networks , 1985, 1985 American Control Conference.

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

[50]  A. Goldsmith,et al.  Kalman filtering with partial observation losses , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[51]  Asok Ray,et al.  An observer-based compensator for distributed delays , 1990, Autom..

[52]  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).