An Approach to Data-Based Linear Quadratic Optimal Control

This letter presents a data-based approach to linear quadratic optimal control design. The system manipulated variable is assumed to have a zero mean uncertainty with a certain covariance, and the true system trajectory is measurable subject to measurement noise. The separation principle in the data-based context is investigated, which reveals that the original problem can be decomposed into an optimal quadratic control problem and an interval-wise trajectory estimation problem that can be designed separately. Algorithms are developed for both the finite and infinite horizon control problem, with the latter proven to be able to asymptotically stabilize the expected value of all trajectories in the controlled behavior. An illustrative example is provided to demonstrate the effectiveness of the proposed approach.