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Operations Research, Systems Engineering and Industrial Engineering Commons

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2008

Physical Sciences and Mathematics

Electrical and Computer Engineering Faculty Research & Creative Works

Generalized Hamilton-Jacobi-Bellman (BHJB) Equation

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Full-Text Articles in Operations Research, Systems Engineering and Industrial Engineering

Generalized Hamilton-Jacobi-Bellman Formulation-Based Neural Network Control Of Affine Nonlinear Discrete-Time Systems, Zheng Chen, Jagannathan Sarangapani Jan 2008

Generalized Hamilton-Jacobi-Bellman Formulation-Based Neural Network Control Of Affine Nonlinear Discrete-Time Systems, Zheng Chen, Jagannathan Sarangapani

Electrical and Computer Engineering Faculty Research & Creative Works

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 ...