Approximate dynamic programming for continuous-time linear quadratic regulator problems: relaxation of known input-coupling matrix assumption

This study proposes an approximate dynamic programming (ADP) scheme which solves approximately the continuous-time (CT) infinite horizon, linear quadratic (LQ) optimal control problems (OCPs) online for CT linear time-invariant (LTI) systems whose model is not exactly given a priori. In order to relax the assumption of the perfectly known input-coupling matrix, a cheap OCP consisting of a dynamic controller and a modified quadratic performance index is formulated from the conventional LQ OCP. Then, the CT ADP technique based on policy iteration is embedded in the controller as an adaptive element for iteratively solving this cheap OCP in online fashion. By solving the cheap OCP, the near-optimal solution of the original LQ OCP can be obtained, which is proven in this study. The proposed scheme guarantees the stability and convergence to a near-optimal solution, and does not require the knowledge regarding system dynamics during the iterations. Finally, the simulation results are provided to verify the applicability and effectiveness of the proposed control scheme.