LQG Control with Missing Observation and Control Packets
| Authors: | Sinopoli Bruno, University of California at Berkeley, United States
Luca Schenato, University of Padova, Italy
Massimo Franceschetti, University of California at San Diego, United States
Kameshwar Poolla, University of California at Berkeley, United States
Shankar Sastry, University of California at Berkeley, United States |
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| Topic: | 2.4 Optimal Control |
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| Session: | Optimal Control in Stochastic Systems |
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| Keywords: | LQG control, optimal control, linear control systems, stochastic control, distributed control |
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Abstract
The paper considers the Linear Quadratic Gaussian (LQG) optimalcontrol problem in the discrete time setting and when data lossmay occur between the sensors and the estimation-control unit andbetween the latter and the actuation points. For protocols wherepackets are acknowledged at the receiver (e.g. TCP typeprotocols), the separation principle holds. Moreover, the optimalLQG control is a linear function of the state. Finally, buildingupon our previous results on estimation with unreliablecommunication, the paper shows the existence of critical arrivalprobabilities below which the optimal controller fails tostabilize the system. This is done by providing analytic upper andand lower bounds on the cost functional, and stochasticallycharacterizing their convergence properties in the infinitehorizon. More interestingly, it turns out that when there is nofeedback on whether a control packet has been delivered ornot (e.g. UDP type protocols), the LQG optimal controller is ingeneral nonlinear.
