Adaptive optimal output regulation of unknown linear continuous-time systems by dynamic output feedback and value iteration

This paper proposes a value iteration based learning algorithm to solve the optimal output regulation problem for linear continuous-time systems, which aims at achieving disturbance rejection and asymptotic tracking simultaneously. Notably, the state is unmeasurable and the system dynamics is completely unknown, which greatly increases the challenge of solving the output regulation problem. Firstly, we present a dynamic output feedback controller design method by combining the internal model, setting a virtual exo-system, and constructing the augmented internal state without using any knowledge of system. Then, by establishing a novel iterative learning equation which requires no repeated finite window integral operations, an adaptive dynamic programming based learning algorithm with employing value-iteration scheme is proposed to estimate the optimal feedback control gain, which may lead to a reduction of the computational load. The analysis on solvability and convergence shows that the estimated control gain converges to the optimal control gain. Finally, a physical experiment on control of an unmanned quadrotor illustrates the effectiveness of the proposed algorithm.