Finite-Horizon H2/H∞ control for discrete-time stochastic systems with multiple decision makers

In this paper, finite-horizon H₂/H_∞ control problems with multiple decision makers are investigated. In contrast to the existing result in Zhang et al., (2007), here we consider multiple controls. First, a necessary condition for the existence of H₂/H_∞ control is established by using a cross-coupled stochastic backward difference Riccati equations (CSBDREs). In particular, both Pareto and Nash strategy sets are established, and it is further shown that the Pareto strategy set is equivalent to the linear quadratic (LQ) game as the cooperative strategy. Lastly, a simple numerical example is given to show the validity and potential of the proposed method.