NDLI: Generalized Hamilton–Jacobi–Bellman Formulation -Based Neural Network Control of Affine Nonlinear Discrete-Time Systems

Content Provider	IEEE Xplore Digital Library
Author	Zheng Chen Jagannathan, S.
Copyright Year	1990
Abstract	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.
Sponsorship	IEEE Computational Intelligence Society
Page Count	17
File Size	1312062
Starting Page	90
Ending Page	106
File Format	PDF
ISSN	10459227
Volume Number	19
Issue Number	1
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2008-01-01
Publisher Place	U.S.A.
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Neural networks Nonlinear control systems Control systems Optimal control Nonlinear equations Riccati equations Least squares approximation Cost function Nonlinear systems Stability nonlinear discrete-time (DT) system Generalized Hamilton–Jacobi–Bellman (BHJB) equation neural network (NN) Generalized Hamilton-Jacobi-Bellman (BHJB) equation
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Computer Networks and Communications Computer Science Applications Software

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