Control Over Lossy Networks: A Dynamic Game Approach

Abstract-- This paper considers a minimax control (H⁾ control) problem for linear time-invariant (LTI) systems where the communication loop is subject to a TCP-like packet drop network. The problem is formulated within the zero-sum dynamic game framework. The packet drop network is governed by two independent Bernoulli processes that model control and measurement packet losses. Under this constraint, we obtain a dynamic output feedback minimax controller. For the infinite-horizon case, we provide necessary and sufficient conditions in terms of the packet loss rates and the H disturbance attenuation parameter under which the minimax controller exists and is able to stabilize the closed-loop system in the mean-square sense. In particular, we show that unlike the corresponding LQG case, these conditions are coupled and therefore cannot be determined independently.