Adaptive Dynamic Programming and Adaptive Optimal Output Regulation of Linear Systems

This note studies the adaptive optimal output regulation problem for continuous-time linear systems, which aims to achieve asymptotic tracking and disturbance rejection by minimizing some predefined costs. Reinforcement learning and adaptive dynamic programming techniques are employed to compute an approximated optimal controller using input/partial-state data despite unknown system dynamics and unmeasurable disturbance. Rigorous stability analysis shows that the proposed controller exponentially stabilizes the closed-loop system and the output of the plant asymptotically tracks the given reference signal. Simulation results on a LCL coupled inverter-based distributed generation system demonstrate the effectiveness of the proposed approach.