Data-driven robust linear quadratic regulator: A minimax design using reinforcement learning
Haoran Ma, Zhengen Zhao, Ying Yang · Automatica · 2025
This paper presents a minimax design approach based on model-free reinforcement learning (RL) to solve the robust linear quadratic regulator (LQR) problem. The proposed method derives a controller that guarantees stability and tends to be optimal as the data amount increases, even in the presence of unknown system dynamics . Initially, the robust LQR problem is transformed into a zero-sum differential game to minimize the worst linear quadratic cost in the system ensemble compatible with data containing Gaussian noise . Then, the RL algorithm is delineated, accompanied by the necessary and sufficient data condition for the existence of a unique solution, which is equivalent to the model-based minimax design solution. The RL-based controller can stabilize the original system with a high probability. Simultaneously, the sub-optimality gap between the controller’s performance and the optimal performance illustrates the asymptotic optimality of the controller. In addition to these attributes, the proposed method exhibits a distinct advantage in terms of computational efficiency. Simulations validate the effectiveness of the proposed method in terms of robustness, optimality, and run time.