Finite‐Horizon ε‐Optimal Tracking Control of Discrete‐Time Linear Systems Using Iterative Approximate Dynamic Programming

Abstract

AbstractIn this paper, we propose a finite‐horizon neuro‐optimal tracking control strategy for a class of discrete‐time linear systems. In applying the iterative approximate dynamic programming (ADP) algorithm to determine the optimal tracking control law for linear systems, we need finite iterations to obtain the result in practical applications, instead of infinite iterations. An ε‐error bound is introduced into the ADP algorithm to determine the number of iteration steps. The approximation optimal tracking control law will approach the solution of the Hamilton‐Jacobi‐Bellman (HJB) equation through a self‐adaptive iteration within the given value of ε‐error bound. ε error bound is used to stop the iteration process. So, we can obtain the ε‐approximation tracking control law in a finite number of iterations. Nevertheless, different ε will produce different control performances. Furthermore, we will find an optimal ε error bound, which can obtain optimal performance of the ADP algorithm on the basis of the controlled system tracking the desired trajectory. One example is included to complete the ADP algorithm under different error bounds. From the simulation results, we can find the optimal ε error bound. Finally, the simulation validates the efficiency of the proposed algorithm.