Multi-objective decision-making problems for discrete-time stochastic systems with state- and disturbance-dependent noise

In this paper, we consider three types of infinite-horizon multi-objective decision-making problems for a class of discrete-time linear stochastic systems with state- and disturbance-dependent noise. First, the H₂/H_∞ control problem with multiple decision makers is considered. Second, in order to improve the transient response, the linear quadratic control under the Pareto solution is investigated. Finally, the soft-constrained stochastic Nash games are formulated in which robustness is attained against disturbance input. The decision strategies for the three types of problem are derived. It is found that the conditions for the existences of these strategies are related to the solutions of cross-coupled stochastic algebraic Riccati equations (CSAREs). We develop some new algorithms based on linear matrix inequality (LMI) to solve the CSAREs. Numerical example is provided to verify the efficiency of the proposed decision strategies.