Alternating Positive and Negative Feedback Control Model Based on Catastrophe Theories

In automatic control systems, negative feedback control has the advantage of maintaining a steady state, while positive feedback control can enhance some activities of the control system. How to design a controller with both control modes is an interesting and challenging problem. Motivated by it, o...

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Autores principales:	Wenkai Huang, Fobao Zhou, Tao Zou, Puwei Lu, Yihao Xue, Jiajian Liang, Yikai Dong
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	adaptive alternating positive and negative feedback adaptive control feedback control catastrophe theory Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/495a02b9679c4666b8c625a39405a991
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spelling	oai:doaj.org-article:495a02b9679c4666b8c625a39405a9912021-11-25T18:16:51ZAlternating Positive and Negative Feedback Control Model Based on Catastrophe Theories10.3390/math92228782227-7390https://doaj.org/article/495a02b9679c4666b8c625a39405a9912021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2878https://doaj.org/toc/2227-7390In automatic control systems, negative feedback control has the advantage of maintaining a steady state, while positive feedback control can enhance some activities of the control system. How to design a controller with both control modes is an interesting and challenging problem. Motivated by it, on the basis idea of catastrophe theories, taking positive feedback and negative feedback as two different states of the system, an adaptive alternating positive and negative feedback (APNF) control model with the advantages of two states is proposed. By adaptively adjusting the relevant parameters of the constructed symmetric catastrophe function and the learning rule based on error and forward weight, the two states can be switched in the form of catastrophe. Through the Lyapunov stability theory, the convergence of the proposed adaptive APNF control model is proven, which indicates that system convergence can be guaranteed by selecting appropriate parameters. Moreover, we present theoretical proof that the negative feedback system with negative parameters can be equivalent to the positive feedback system with positive parameters. Finally, the results of the simulation example show that APNF control has satisfactory performance in response speed and overshoot.Wenkai HuangFobao ZhouTao ZouPuwei LuYihao XueJiajian LiangYikai DongMDPI AGarticleadaptive alternating positive and negative feedbackadaptive controlfeedback controlcatastrophe theoryMathematicsQA1-939ENMathematics, Vol 9, Iss 2878, p 2878 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	adaptive alternating positive and negative feedback adaptive control feedback control catastrophe theory Mathematics QA1-939
spellingShingle	adaptive alternating positive and negative feedback adaptive control feedback control catastrophe theory Mathematics QA1-939 Wenkai Huang Fobao Zhou Tao Zou Puwei Lu Yihao Xue Jiajian Liang Yikai Dong Alternating Positive and Negative Feedback Control Model Based on Catastrophe Theories
description	In automatic control systems, negative feedback control has the advantage of maintaining a steady state, while positive feedback control can enhance some activities of the control system. How to design a controller with both control modes is an interesting and challenging problem. Motivated by it, on the basis idea of catastrophe theories, taking positive feedback and negative feedback as two different states of the system, an adaptive alternating positive and negative feedback (APNF) control model with the advantages of two states is proposed. By adaptively adjusting the relevant parameters of the constructed symmetric catastrophe function and the learning rule based on error and forward weight, the two states can be switched in the form of catastrophe. Through the Lyapunov stability theory, the convergence of the proposed adaptive APNF control model is proven, which indicates that system convergence can be guaranteed by selecting appropriate parameters. Moreover, we present theoretical proof that the negative feedback system with negative parameters can be equivalent to the positive feedback system with positive parameters. Finally, the results of the simulation example show that APNF control has satisfactory performance in response speed and overshoot.
format	article
author	Wenkai Huang Fobao Zhou Tao Zou Puwei Lu Yihao Xue Jiajian Liang Yikai Dong
author_facet	Wenkai Huang Fobao Zhou Tao Zou Puwei Lu Yihao Xue Jiajian Liang Yikai Dong
author_sort	Wenkai Huang
title	Alternating Positive and Negative Feedback Control Model Based on Catastrophe Theories
title_short	Alternating Positive and Negative Feedback Control Model Based on Catastrophe Theories
title_full	Alternating Positive and Negative Feedback Control Model Based on Catastrophe Theories
title_fullStr	Alternating Positive and Negative Feedback Control Model Based on Catastrophe Theories
title_full_unstemmed	Alternating Positive and Negative Feedback Control Model Based on Catastrophe Theories
title_sort	alternating positive and negative feedback control model based on catastrophe theories
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/495a02b9679c4666b8c625a39405a991
work_keys_str_mv	AT wenkaihuang alternatingpositiveandnegativefeedbackcontrolmodelbasedoncatastrophetheories AT fobaozhou alternatingpositiveandnegativefeedbackcontrolmodelbasedoncatastrophetheories AT taozou alternatingpositiveandnegativefeedbackcontrolmodelbasedoncatastrophetheories AT puweilu alternatingpositiveandnegativefeedbackcontrolmodelbasedoncatastrophetheories AT yihaoxue alternatingpositiveandnegativefeedbackcontrolmodelbasedoncatastrophetheories AT jiajianliang alternatingpositiveandnegativefeedbackcontrolmodelbasedoncatastrophetheories AT yikaidong alternatingpositiveandnegativefeedbackcontrolmodelbasedoncatastrophetheories
_version_	1718411376613916672

Alternating Positive and Negative Feedback Control Model Based on Catastrophe Theories

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