Remote Robust Optimal State Estimation for Discrete-Time Systems Over Markovian Lossy Channels

Networked control systems (NCS) have received increasing attention from many communities over the recent decades, and the use of network devices with limited capacities brings significant challenges to conventional system design. This paper is focused on the remoteH_∞Gaussian state estimation problem for discrete-time systems over unreliable communication channels within the framework of Nash game, where the packet dropouts are characterized by Markov processes. The mean square (MS) stability of estimation error dynamics is proven based on a set of cross-coupled modified algebraic Riccati equations (MAREs), and the resulting Nash equilibrium strategies, including the worst-case disturbance signal and the optimal filter gain, are also established. The developed filter is able to ensure robustness against disturbance/modeling uncertainties and to obtain the minimized variance of the state estimation error under the worst-case disturbance. Moreover, a necessary condition and a sufficient condition concerning the fundamental limits of data failure rates on the MS stability of error dynamics are conducted in terms of unstable poles of the plant and statistical characteristics of the communication channels. We further explore the solvability conditions of MAREs associated with single robust or optimal performance for scalar systems. Finally, a numerical example is also provided to illustrate the effectiveness of the current results.