An Adaptive Dynamic Programming Scheme for Nonlinear Optimal Control With Unknown Dynamics and Its Application to Turbofan Engines - Sun, Tao; Sun, Xi-Ming (IEEE transactions on industrial informatics, 2021)
In this article, a novel adaptive dynamic programming (ADP) approach is proposed for the optimal control problem of nonlinear continuous control systems with unknown dynamics. First, an alternating iteration algorithm based on Hamilton-Jacobi-Bellman equation is proposed for the optimal control of known nonlinear control systems. Then, the convergence results of the alternating iteration algorithm are obtained by using mathematical induction and monotone bounded convergence theorem. Moreover, the global asymptotic stability of the nonlinear closed-loop system is proved. Second, based on the scheme of alternating iteration algorithm, an ADP algorithm for the optimal control problem with unknown nonlinear dynamic model is developed by using the basis function approximation method and Newton-Leibniz formula, which can update the control strategy online by utilizing input and output information of the system. In addition, the convergence analysis of the proposed ADP algorithm is derived. Finally, the feasibility of the established results is verified by two examples, and the ADP method is applied to the optimal tracking fuel control problem of turbofan engines.