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LQG control on mixed H2/H∞ problem: the discrete-time case

ABSTRACT In this paper, we are concerned with linear quadratic Gaussian (LQG) control on the mixed problem. The mixed problem can be formulated as a kind of constraint optimisation problems where the control input is to minimise the -norm subject to the -constraint dealt with by the disturbance. The main contributions are twofold. First, when the state variables can be obtained exactly, necessary and sufficient conditions are given to guarantee the existence of the strategies. Second, the optimal LQG controller in terms of three decoupled equations (two Riccati equations and one Lyapunov equation) is obtained. The key technique is to apply the Stackelberg game approach by treating the disturbance as the follower and the control input as the leader respectively. A practical example is given to verify the efficiency of the proposed approach.