Fixed-Final-Time-Constrained Optimal Control of Nonlinear Systems Using Neural Network HJB Approach

Author

Cheng, Tao ; Lewis, Frank L. ; Abu-Khalaf, Murad

Author_Institution

Univ. of Texas at Arlington, Fort Worth

Volume

18

Issue

6

fYear

2007

Firstpage

1725

Lastpage

1737

Abstract

In this paper, fixed-final time-constrained optimal control laws using neural networks (NNS) to solve Hamilton-Jacobi-Bellman (HJB) equations for general affine in the constrained nonlinear systems are proposed. An NN is used to approximate the time-varying cost function using the method of least squares on a predefined region. The result is an NN nearly -constrained feedback controller that has time-varying coefficients found by a priori offline tuning. Convergence results are shown. The results of this paper are demonstrated in two examples, including a nonholonomic system.

Keywords

convergence of numerical methods; feedback; least squares approximations; neurocontrollers; nonlinear differential equations; nonlinear dynamical systems; optimal control; time-varying systems; Hamilton-Jacobi-Bellman equation; convergence; feedback controller; fixed-final-time-constrained optimal control; least square method; neural network; nonholonomic system; nonlinear system; time-varying cost function; Constrained input systems; Hamilton–Jacobi–Bellman (HJB); Hamilton-Jacobi-Bellman (HJB); finite-horizon optimal control; neural network (NN) control;

fLanguage

English

Journal_Title

Neural Networks, IEEE Transactions on

Publisher

ieee

ISSN

1045-9227

Type

jour

DOI

10.1109/TNN.2007.905848

Filename

4359214