Optimal LQG control over continuous fading channels

Abstract This paper studies the optimal control of linear systems over continuous valued fading channels. The sensor measurements are sent over a fading wireless channel to a remote controller using the analog amplify and forward technique. The controller then computes a control signal, which is transmitted over another fading channel to the actuator. Under the assumption of full channel state information (CSI) for both wireless links, we derive the optimal LQG control law. In the case where full channel state information is not available but channel statistics are available, we present the optimal linear static estimator and controller. Numerical comparisons are made between the full CSI and statistical CSI solutions.

[1]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

[2]  H. Chizeck,et al.  Optimal quadratic control of jump linear systems with Gaussian noise in discrete-time , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

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

[4]  Y. Mostofi,et al.  On dropping noisy packets in Kalman filtering over a wireless fading channel , 2005, Proceedings of the 2005, American Control Conference, 2005..

[5]  Subhrakanti Dey,et al.  Stability of Kalman filtering with Markovian packet losses , 2007, Autom..

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

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

[8]  L. Schenato.  Optimal estimation in networked control systems subject to random delay and packet loss , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[9]  Luca Schenato,et al.  Optimal Estimation in Networked Control Systems Subject to Random Delay and Packet Drop , 2008, IEEE Transactions on Automatic Control.

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

[11]  J.P. Hespanha,et al.  Estimation under uncontrolled and controlled communications in Networked Control Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[12]  Petros G. Voulgaris,et al.  On optimal ℓ∞ to ℓ∞ filtering , 1995, Autom..

[13]  Giuseppe Caire,et al.  Optimum power control over fading channels , 1999, IEEE Trans. Inf. Theory.

[14]  Jamie S. Evans,et al.  Kalman filtering with faded measurements , 2009, Autom..

[15]  Ling Shi,et al.  Probabilistic performance of state estimation across a lossy network , 2008, Autom..

[16]  W. L. Koning,et al.  Compensatability and optimal compensation of systems with white parameters , 1992 .

[17]  Michael Gastpar,et al.  Source-Channel Communication in Sensor Networks , 2003, IPSN.

[18]  Andrea J. Goldsmith,et al.  Estimation Diversity and Energy Efficiency in Distributed Sensing , 2007, IEEE Transactions on Signal Processing.

[19]  S. Sastry,et al.  Optimal control with unreliable communication: the TCP case , 2005, Proceedings of the 2005, American Control Conference, 2005..

[20]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .