Model-Free Inverse Optimal Control for Completely Unknown Nonlinear Systems by Adaptive Dynamic Programming

This article presents an inverse optimal control (IOC) approach for nonlinear polynomial systems based on adaptive dynamic programming (ADP). First, a novel model-based algorithm is presented which provides a control policy, a suboptimal Lyapunov function, and an objective function, that is, minimized by applying the control policy. It is then extended to a model-free approach for systems with a completely unknown model using only the measured input/output data. Compared with existing ADP-based algorithms for nonlinear continuous-time systems, the proposed algorithm is data-based and does not rely on numerical solutions for model approximation. Additionally, it is an off-policy algorithm and avoids the repeat of experiments for control design. Instead, an ADP-based sum-of-squares programming is presented which is computationally tractable. The theoretical guarantee for the stability of the proposed IOC is established using the Lyapunov technique. The performance and efficacy of the proposed approach are investigated through three simulation examples.