Multi-objective optimal control for a class of unknown nonlinear systems based on finite-approximation-error ADP algorithm

Abstract

In this paper, an optimal control method for a class of unknown discrete-time nonlinear systems with general multi-objective performance indices is proposed. In the design of the optimal controller, only available input–output data are required instead of known system dynamics, and the data-based identifier is established with stability proof. By the weighted sum technology, the multi-objective optimal control problem is transformed into the single objective optimization. To obtain the solution of the HJB equation, the novel finite-approximation-error adaptive dynamic programming (ADP) algorithm is presented with convergence proof. The detailed theoretic analyses for the relationship of the approximation accuracy and the algorithm convergence are given. It is shown that, as convergence conditions are satisfied, the iterative performance index functions can converge to a finite neighborhood of the greatest lower bound of all performance index functions. Neural networks are used to approximate the performance index function and compute the optimal control policy, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the proposed method.