Optimal dynamic output feedback control of unknown linear continuous-time systems by adaptive dynamic programming

In this paper, we present an approximate optimal dynamic output feedback control learning algorithm to solve the linear quadratic regulation problem for unknown linear continuous-time systems. First, a dynamic output feedback controller is designed by constructing the internal state. Then, an adaptive dynamic programming based learning algorithm is proposed to estimate the optimal feedback control gain by only accessing the input and output data. By adding a constructed virtual observer error into the iterative learning equation, the proposed learning algorithm with the new iterative learning equation is immune to the observer error. In addition, the value iteration based learning equation is established without storing a series of past data, which could lead to a reduction of demands on the usage of memory storage. Besides, the proposed algorithm eliminates the requirement of repeated finite window integrals, which may reduce the computational load. Moreover, the convergence analysis shows that the estimated control policy converges to the optimal control policy. Finally, a physical experiment on an unmanned quadrotor is given to illustrate the effectiveness of the proposed approach.