LQG control with Markovian packet loss

This paper is concerned with the optimal LQG control of a system through lossy data networks. In particular we will focus on the case where control commands are issued to the system over a communication network where packets may be randomly dropped according to a two-state Markov chain. Under these assumptions, the optimal finite-horizon LQG problem is solved by means of dynamic programming arguments. The infinite horizon LQG control problem is explored and conditions to ensure its convergence are investigated. Finally it is shown how the results presented in this paper can be employed in the case that also the observation packet may be dropped. A numerical simulation shows the relationship between the convergence of the LQG cost and the value of the parameters of the Markov chain.