Data-driven optimal tracking control for nonlinear systems with performance constraints via adaptive dynamic programming.

Abstract

This paper studies the optimal tracking problem for an unknown nonlinear systems subject to input and performance constraints. A data-driven constrained optimal tracking control scheme is designed to make the system states pursue the desired trajectory while minimizing the cost and strictly limiting the tracking error within thepredefined zones. Specifically, a finite-time performance function is deployed to ensure that errors converge to steady-state regions within a user-defined time. Furthermore, by employing a nonquadratic cost function, a modified Hamilton-Jacobi-Bellman equation is constructed to ensure input limitations are satisfied. Subsequently, the adaptive dynamic programming algorithm, implemented with neural networks (NNs) in an actor-critic structure, is employed to learn the optimal control policy without relying on any prior information about the system dynamics. Meanwhile, the weights of the actor-critic NNs are tuned using the least-squares method based on the collected dataset. Finally, simulations on Chua's circuit demonstrate the effectiveness and benefits of the designed algorithm.