Data-driven optimal control with reduced output measurements

This paper uses the integral reinforcement learning (IRL) technique to develop an online learning algorithm for finding suboptimal static output-feedback controllers for partially-unknown continuous-time (CT) linear systems. To our knowledge, this is the first static output-feedback control design method based on reinforcement learning for CT systems. In the proposed method, an online policy iteration (PI) algorithm is developed which uses the integral reinforcement knowledge for learning a suboptimal static output-feedback solution without requiring the drift knowledge of the system dynamics. Specifically, in the policy evaluation step of the PI algorithm, an IRL Bellman equation is used to evaluate an output-feedback policy, and in the policy improvement step of the PI algorithm the output-feedback gain is updated using the information given by the evaluated policy. An adaptive observer is used to provide the knowledge of the full states for the IRL Bellman equation during learning. However, the observer is not needed after the learning process is finished. The convergence of the proposed algorithm to a suboptimal output-feedback solution and the performance of the proposed method are verified through simulations.