A novel optimal tracking control scheme for a class of discrete-time nonlinear systems using generalised policy iteration adaptive dynamic programming algorithm

ABSTRACT

In this paper, a novel iterative adaptive dynamic programming (ADP) algorithm, called generalised policy iteration ADP algorithm, is developed to solve optimal tracking control problems for discrete-time nonlinear systems. The idea is to use two iteration procedures, including an i-iteration and a j-iteration, to obtain the iterative tracking control laws and the iterative value functions. By system transformation, we first convert the optimal tracking control problem into an optimal regulation problem. Then the generalised policy iteration ADP algorithm, which is a general idea of interacting policy and value iteration algorithms, is introduced to deal with the optimal regulation problem. The convergence and optimality properties of the generalised policy iteration algorithm are analysed. Three neural networks are used to implement the developed algorithm. Finally, simulation examples are given to illustrate the performance of the present algorithm.

KEYWORDS:

• Adaptive dynamic programming
• affine nonlinear systems
• discrete-time
• generalised policy iteration
• neural network
• tracking control

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [grant numbers 61233001, 61273140, 61304086, 61374105, and 61533017] in part by Beijing Natural Science Foundation [grant number 4132078], and in part by the Early Career Development Award of SKLMCCS.