Game-based multi-objective evolution of robust controllers

This paper focuses on the design of controllers that are robust to external noise. A novel framework based on multi-objective games is proposed to address this challenge. A model of a two-player Stackelberg game is employed. The first player is a decision-maker who seeks to find an optimal controller. The second player is a noise generator that simultaneously optimizes the external noise to identify the most disruptive noise profiles. Following the Stackelberg game model, the noise generator's strategies (noise profiles) are evaluated only against the controllers that the decision-maker selects. Therefore, this approach is expected to be more computationally efficient. A modified co-evolutionary algorithm is then developed to solve this game. Through a numerical study on a robust control problem, the effectiveness of the proposed approach (and algorithm) in identifying a non-dominated set of robust solutions is demonstrated, showcasing its superiority over traditional methods.