PID Controller Singularly Perturbing Impulsive Differential Equations and Optimal Control Problem

PID Controller Singularly Perturbing Impulsive Differential Equations and Optimal Control Problem

We study singular perturbation of impulsive system with a proportional-integral-derivative controller (PID controller) and solve an optimal control problem. The perturbation system comprises two important variables, a fast variable and a slow variable. Because of the complexity of the system, it is...

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Main Author: Wichai Witayakiattilerd
Format: Article
Language:English
Published: Hindawi Limited 2017-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2017/1938513
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spelling doaj-daef5004e9e64a21a3135f17b3f2bff62021-07-02T09:02:06ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/19385131938513PID Controller Singularly Perturbing Impulsive Differential Equations and Optimal Control ProblemWichai Witayakiattilerd0Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Paholyothin Road, Klong Luang, Rangsit, Pathumthani 12121, ThailandWe study singular perturbation of impulsive system with a proportional-integral-derivative controller (PID controller) and solve an optimal control problem. The perturbation system comprises two important variables, a fast variable and a slow variable. Because of the complexity of the system, it is difficult to find its exact solution. This paper presents an approximation method for solving it. The aim of the approximation method is to reduce the complexity of the system by eliminating the fast variable. The solution of the method is expressed in an integral form, and it is called an approximated mild solution of the perturbed system. An example is provided to illustrate our result.http://dx.doi.org/10.1155/2017/1938513
collection DOAJ
language English
format Article
sources DOAJ
author Wichai Witayakiattilerd
spellingShingle Wichai Witayakiattilerd
PID Controller Singularly Perturbing Impulsive Differential Equations and Optimal Control Problem
Advances in Mathematical Physics
author_facet Wichai Witayakiattilerd
author_sort Wichai Witayakiattilerd
title PID Controller Singularly Perturbing Impulsive Differential Equations and Optimal Control Problem
title_short PID Controller Singularly Perturbing Impulsive Differential Equations and Optimal Control Problem
title_full PID Controller Singularly Perturbing Impulsive Differential Equations and Optimal Control Problem
title_fullStr PID Controller Singularly Perturbing Impulsive Differential Equations and Optimal Control Problem
title_full_unstemmed PID Controller Singularly Perturbing Impulsive Differential Equations and Optimal Control Problem
title_sort pid controller singularly perturbing impulsive differential equations and optimal control problem
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2017-01-01
description We study singular perturbation of impulsive system with a proportional-integral-derivative controller (PID controller) and solve an optimal control problem. The perturbation system comprises two important variables, a fast variable and a slow variable. Because of the complexity of the system, it is difficult to find its exact solution. This paper presents an approximation method for solving it. The aim of the approximation method is to reduce the complexity of the system by eliminating the fast variable. The solution of the method is expressed in an integral form, and it is called an approximated mild solution of the perturbed system. An example is provided to illustrate our result.
url http://dx.doi.org/10.1155/2017/1938513
work_keys_str_mv AT wichaiwitayakiattilerd pidcontrollersingularlyperturbingimpulsivedifferentialequationsandoptimalcontrolproblem
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