Asymptotic policies for stochastic differential linear quadratic games with intermittent state feedback

Abstract

In this paper, we consider infinite horizon linear quadratic stochastic differential games where the games are neither open-loop nor closed-loop. The state of the game dynamics is measured only when a certain switch is closed. The switch requires unanimous operation by the players, and continuum state measurements are not possible. There is an upper bound on the number of times the switch can be closed. Each player is given a quadratic cost function and the objective of each player is to design a switching strategy and a control strategy in order to optimize their respective cost function. We investigate the Nash control strategy and optimal switching policy for this game with two different cost structures: discounted cost and average-time cost.