In this paper, we consider the use of nonlinear networks towards obtaining nearly optimal solutions to the control of nonlinear discrete-time (DT) systems. The method is based on least squares successive approximation solution of the generalized Hamilton-Jacobi-Bellman (GHJB) equation which appears in optimization problems. Successive approximation using the GHJB has not been applied for nonlinear DT systems. The proposed recursive method solves the GHJB equation in DT on a well-defined region of attraction. The definition of GHJB, pre-Hamiltonian function, HJB equation, and method of updating the control function for the affine nonlinear DT systems under small perturbation assumption are proposed. A neural network (NN) is used to approximate the GHJB solution. It is shown that the result is a closed-loop control based on an NN that has been tuned a priori in offline mode. Numerical examples show that, for the linear DT system, the updated control laws will converge to the optimal control, and for nonlinear DT systems, the updated control laws will converge to the suboptimal control.


Electrical and Computer Engineering

Second Department

Computer Science

Keywords and Phrases

Generalized Hamilton-Jacobi-Bellman (BHJB) Equation; Neural Network (NN); Nonlinear Discrete-Time (DT) System

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version

Final Version

File Type





© 2008 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Jan 2008