Estimation and Control over Lossy Networks

Motivated by control applications over lossy packet networ ks, this paper considers the Linear Quadratic Gaussian (LQG) optimal control problem in the dis crete time setting and when packet losses may occur between the sensors and the estimation-con trol u it and between the latter and the actuation points. Previous work [1] shows that, for protoco ls where packets are acknowledged at the receiver (e.g. TCP-like protocols), the separation princi ple holds. Moreover, in this case the optimal LQG control is a linear function of the estimated state and th ere exist critical probabilities for the successful delivery of both observation and control packet s, below which the optimal controller fails to stabilize the system. The existence of such critical valu es is determined by providing analytic upper and lower bounds on the cost functional, and stochasti cally characterizing their convergence properties in the infinite horizon. Finally, it turns out tha when there is no feedback on whether a control packet has been delivered or not (e.g. UDP-like prot oc ls), the LQG optimal controller is in general nonlinear, as also shown in [2].