Fractional Order Version of the Hamilton–Jacobi–Bellman Equation-Reference-Cited by-同舟云学术

Fractional Order Version of the Hamilton–Jacobi–Bellman Equation

Published:2018-11-28 Issue:1 Volume:14 Page:
ISSN:1555-1415
Container-title:Journal of Computational and Nonlinear Dynamics
language:en
Short-container-title:

Author:

Razminia Abolhassan¹,Asadizadehshiraz Mehdi²,Torres Delfim F. M.³

Affiliation:

1. Electrical Engineering Department, School of Engineering, Persian Gulf University, P.O. Box 75169, Bushehr 75169-13817, Iran e-mail:

2. Electronic and Electrical Engineering Department, Shiraz University of Technology, P.O. Box 71555-313 Shiraz 71557-13876, Iran e-mail:

3. R&D Unit CIDMA, Department of Mathematics, Center for Research and Development in Mathematics and Applications, University of Aveiro, Aveiro 3810-193, Portugal e-mail:

Abstract

We consider an extension of the well-known Hamilton–Jacobi–Bellman (HJB) equation for fractional order dynamical systems in which a generalized performance index is considered for the related optimal control problem. Owing to the nonlocality of the fractional order operators, the classical HJB equation, in the usual form, does not hold true for fractional problems. Effectiveness of the proposed technique is illustrated through a numerical example.

Funder

Fundação para a Ciência e a Tecnologia

Publisher

ASME International

Subject

Applied Mathematics,Mechanical Engineering,Control and Systems Engineering,Applied Mathematics,Mechanical Engineering,Control and Systems Engineering

Link

http://asmedigitalcollection.asme.org/computationalnonlinear/article-pdf/doi/10.1115/1.4041912/6112124/cnd_014_01_011005.pdf

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