Data-based constrained optimal control for completely unknown nonlinear time-varying systems

Although the model-based control for nonlinear time-varying (NTV) systems is a challenging problem, this paperproposes a data-based approach to solve the constrained optimal control problem for continuous-time nonlinear polynomial time-varying systems with completely unknown dynamics. This approach does not rely on computationally expensive numerical solutions for model approximation methods. Instead, the optimal control policy is obtained by an adaptive dynamic programming (ADP)-based sum-of-squares (SOS) programming which is computationally tractable. The proposed model-free optimal control approach can apply constraints on the control input. By a novel idea, the input limitations are applied using the concept of inverse optimal control (IOC). The Lyapunov method theoretically ensures the stability of the proposed optimal control scheme. Additionally, it is an off-policy algorithm and avoids the repeat of experiments for control design. The efficacy of the suggested method is investigated through two numerical examples.