Data‐Driven Adaptive Critic Approach for Nonlinear Optimal Control via Least Squares Support Vector Machine

Abstract

This paper develops an online adaptive critic algorithm based on policy iteration for partially unknown nonlinear optimal control with infinite horizon cost function. In the proposed method, only a critic network is established, which eliminates the action network, to simplify its architecture. The online least squares support vector machine (LS-SVM) is utilized to approximate the gradient of the associated cost function in the critic network by updating the input-output data. Additionally, a data buffer memory is added to alleviate computational load. Finally, the feasibility of the online learning algorithm is demonstrated in simulation on two example systems.

Adaptive predictive path following control based on least squares support vector machines for underactuated autonomous vessels

“…subject to (17). Problem (18) is a nonlinear programming problem since cost function (16) and constraint (15) are nonlinear. The algorithm of predictive path following is summarized in Algorithm 1.…”

“…The method of support vector machines (SVM) is introduced for classification and function estimation based on structural risk minimization principle in [13,14]. SVM solutions are characterized by convex optimization problems to avoid local minimums with classical neural networks approaches [15,16]. Least squares support vector machines (LS-SVM) based classifiers were proposed by Suykens [17], which works with equality constraints instead of inequality constraints and a sum squared error cost function (SSE).…”

Compensator-based approximate optimal control for affine nonlinear systems with input constraints and unmatched disturbances

“…It is considered to be an effective technique to find the solution of the HJB equation. Therefore, in recent years, research on ADP and related fields has gained much attention, and considerable efforts have been made (Lv et al, 2016; Modares et al, 2014; Sun et al, 2018; Wen et al, 2019; X. Yang et al, 2019; Y. Yang et al, 2019).…”

Numerical solution of optimal control problems governed by integro‐differential equations

“…Various types of optimal control problems have been investigated by these methods. Up to now, much effort has been committed to the development of various approaches for solving optimal control problems governed by ordinary differential equations [5][6][7][8][9][10][11][12][13][14]. However, a few research works have been devoted to the theoretical aspects and numerical investigation of optimal control problems described by integro-differential equations such as dynamic programming [15], direct methods based on Legendre's polynomials [16], Chebyshev's polynomials [17,18], Legendre pseudospectral approach [19], and Chebyshev pseudospectral method [20].…”