Journal of Vibration and Control, ( ISI ), Volume (1), No (1), Year (2016-9) , Pages (1-16)

Title : ( Solving a class of fractional optimal control problems by the Hamilton–Jacobi–Bellman equation )

Authors: Seyed Ali Rakhshan , Sohrab Effati , Ali Vahidian Kamyad ,

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The performance index of both the state and control variables with a constrained dynamic optimization problem of a fractional order system with fixed final Time have been considered here. This paper presents a general formulation and solution scheme of a class of fractional optimal control problems. The method is based upon finding the numerical solution of the Hamilton–Jacobi–Bellman equation, corresponding to this problem, by the Legendre–Gauss collocation method. The main reason for using this technique is its efficiency and simple application. Also, in this work, we use the fractional derivative in the Riemann–Liouville sense and explain our method for a fractional derivative of order of Formula . Numerical examples are provided to show the effectiveness of the formulation and solution scheme.

Keywords

Fractional optimal control problem Riemann–Liouville fractional derivative Hamilton–Jacobi–Bellman equation linear quadratic regulator system Legendre–Gauss
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@article{paperid:1058232,
author = {Rakhshan, Seyed Ali and Effati, Sohrab and Vahidian Kamyad, Ali},
title = {Solving a class of fractional optimal control problems by the Hamilton–Jacobi–Bellman equation},
journal = {Journal of Vibration and Control},
year = {2016},
volume = {1},
number = {1},
month = {September},
issn = {1077-5463},
pages = {1--16},
numpages = {15},
keywords = {Fractional optimal control problem Riemann–Liouville fractional derivative Hamilton–Jacobi–Bellman equation linear quadratic regulator system Legendre–Gauss collocation},
}

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%0 Journal Article
%T Solving a class of fractional optimal control problems by the Hamilton–Jacobi–Bellman equation
%A Rakhshan, Seyed Ali
%A Effati, Sohrab
%A Vahidian Kamyad, Ali
%J Journal of Vibration and Control
%@ 1077-5463
%D 2016

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