A new approach of optimal control for a class of continuous-time chaotic systems by an online ADP algorithm

Abstract

We develop an online adaptive dynamic programming (ADP) based optimal control scheme for continuous-time chaotic systems. The idea is to use the ADP algorithm to obtain the optimal control input that makes the performance index function reach an optimum. The expression of the performance index function for the chaotic system is first presented. The online ADP algorithm is presented to achieve optimal control. In the ADP structure, neural networks are used to construct a critic network and an action network, which can obtain an approximate performance index function and the control input, respectively. It is proven that the critic parameter error dynamics and the closed-loop chaotic systems are uniformly ultimately bounded exponentially. Our simulation results illustrate the performance of the established optimal control method.In this section, the optimal control design method using the ADP will be established. As we know, the critic network and the action network are two vital modules of the ADP method that are used to obtain the performance index function ( ) and the control input ( ), respectively. Two neural networks are used as the critic network and the action network. The whole structure is shown in Fig. 1. action network chaotic systems u x utility function critic network J U Fig. 1. The whole structure of the proposed online ADP algorithm.

A novel stable value iteration-based approximate dynamic programming algorithm for discrete-time nonlinear systems

“…The iterative value functions and control laws are obtained iteratively, and the iterative control laws must stabilize the system. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] An initial stabilizing control law is required, however, it is often difficult to obtain. While in most applications, fewer iterations are required, and computationally demanding is more than that of the VI iteration algorithm.…”

Chaotic system optimal tracking using data-based synchronous method with unknown dynamics and disturbances

“…[5] And then the concept of the generalized Lorenz system was extended by Lü, and a class of generalized Lorenz-like systems was discussed. [6] Until now, many efficient approaches have been proposed for controlling chaotic systems, such as impulsive control method, [7][8][9] adaptive dynamic programming (ADP) method, [10] and neural adaptive control. [11] Most of these methodologies consider the chaotic system without disturbance.…”

Policy iteration optimal tracking control for chaotic systems by using an adaptive dynamic programming approach

“…Iterative methods are also used in ADP to obtain the solution of the HJB equation indirectly and they have received increasing attention. [32][33][34][35][36][37][38][39][40] There are two main iterative ADP algorithms, [41] which are based on value and policy iterations, respectively.…”