Composite control of linear quadratic games in delta domain with disturbance observers

In this paper, the disturbance-observer-based composite control problem is investigated for a class of delta domain linear quadratic game with both matched and unmatched disturbances. In the presence of the disturbances, the ϵ-Nash Equilibrium (ϵ-NE) is proposed to describe the outcome of the game. We aim to develop a composite control strategy integrating the disturbance-observer-based control and the feedback Nash strategies such that the matched disturbance is compensated and the individual cost function of each player is optimized. Sufficient conditions are given to ensure the existence of both the desired disturbance observer and the feedback Nash strategies in the delta domain, and then the explicit expressions of the observer gain and Nash strategies are provided. An upper bound for the ϵ-NE is given analytically which demonstrates the robustness of the Nash equilibrium. Finally, a simulation example on the two-area load frequency control problem is provided to illustrate the effectiveness of the proposed design procedure.