Dynamic Feedback Strategies Design of Discrete-Time Game-Based Control Systems

In this paper, a reformulated game-based control system (GBCS) involving a hierarchical decision-making structure with multiple regulators at the upper level and multiple rational agents as followers at the lower level is proposed and its optimal feedback strategies are designed. The regulators are regarded as global controllers that make decisions first, aiming to optimize the macro-performance from their own perspective, and then the followers act and optimize their own objective functions to reach a possible equilibrium. The equilibrium of the GBCS is analyzed within finite horizons with all players' information structure given by a dynamic feedback information pattern. An algorithm is proposed to find the optimal dynamic feedback strategies of all players. Conditions for the existence of the equilibrium are also derived. An illustrative simulation example is given to further demonstrate the effectiveness of the developed algorithm.