H_∞ Optimal Output Regulation of Unknown Linear Systems via an Adaptive Dynamic Programming and Internal Model

This paper delves into the H_∞ optimal output regulation problem for continuous-time linear systems with an unknown system model. By integrating the internal model principle with optimal control, we derive an optimal control policy and a worst-case disturbance policy through the formulation and solution of a zero-sum game problem. Subsequently, leveraging adaptive dynamic programming, we propose a policy iteration learning algorithm capable of learning both the optimal control policy and the worst-case disturbance policy directly from system data. The existing algorithms necessitate an initial stabilizing policy, a full-rank condition, and the storage of historical data to guarantee algorithm convergence. In contrast, we design a dual policy iteration algorithm equipped with an online learning mechanism, thereby eliminating these additional prerequisites. Simulation results with an autonomous ground vehicle underscore the effectiveness of our proposed algorithm, and its superiority is further demonstrated through comparisons with existing methodologies.