Soft-constrained robust equilibria in stochastic differential games

In this paper, infinite-horizon soft-constrained robust equilibria in stochastic differential games are investigated for the Markov jump systems governed by Itô-type stochastic differential equations with state, control and external disturbance-dependent noise. It is shown that the saddle point equilibrium under consideration is associated with the sets of cross-coupled stochastic algebraic Riccati equations (CSAREs). After studying the saddle point solution for a single decision maker case, a multiple decision making problem is considered. A necessary condition for the existence of the robust saddle point equilibrium is found. In particular, it is noteworthy that our new results completely involve some existing results on soft-constrained stochastic Nash game. Finally, a numerical example to verify the efficiency of the proposed algorithms is given.