H2/H∞ control of stochastic systems with multiple decision makers: A Stackelberg game approach

In this paper, H
₂
/H
_∞
control problem for linear stochastic system governed by Itô differential equation with state and external disturbance dependent noise involving multiple decision makers is investigated. A novel strategy concept for reliable decision is that Stackelberg game strategy is applied. As a result, the decision makers are able to induce the disturbance as if the disturbance is optimizing the cost function of each decision maker in hierarchical. It is shown that the required strategy set can be obtained by solving cross-coupled algebraic nonlinear matrix equations (CANMEs). In order to obtain a solution set, a numerical algorithm is derived via LMI technique. A simple numerical example is given to demonstrate the efficiency of the proposed method.