Model-free multiobjective approximate dynamic programming for discrete-time nonlinear systems with general performance index functions

In this paper, a forward-in-time optimal control method for a class of discrete-time nonlinear systems with general multiobjective performance indices is proposed with unknown system dynamics. The proposed approximate dynamic programming (ADP) method aims to find out the increments of both the controls and states instead of computing the controls and states directly. Using the technique of dimension augment, the vector-valued performance indices are transformed into additive quadratic form which satisfies the corresponding discrete-time algebraic Riccati equation (DTARE). Both the action and critic networks can be adaptively tuned by adaptive critic methods without the information of the system model. The convergence property is guaranteed by a rigorous mathematical proof and finally the simulation results show the effectiveness of the method.