Time varying optimal control with packet losses

The problem of using wireless sensor networks technology for estimation and control of dynamical systems has recently received widespread attention within the scientific community. Classical control theory is in general insufficient to model distributed control problems where issues of communication delay, jitter, and time synchronization between components cannot be ignored. The purpose of this paper is to extend our work on discrete time Kalman filtering with intermittent observations (Sinopoli et al., 2004) that was motivated by data losses in a communication channel. Accordingly, we consider the linear Gaussian quadratic (LQG) optimal control problem in the discrete time setting, showing that the separation principle holds in the presence of data losses. Then, using our previous results, we show the existence of a critical arrival probability below which the resulting optimal controller fails to stabilize the system. This is done by providing analytic upper and lower bounds on the cost functional, and stochastically characterizing their convergence properties as k → ∞.