Alternating Positive and Negative Feedback Control Model Based on Catastrophe Theories

Wenkai Huang, Fobao Zhou, Tao Zou, Puwei Lu, Yihao Xue, Jiajian Liang and Yikai Dong
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Wenkai Huang: School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China
Fobao Zhou: School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China
Tao Zou: School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China
Puwei Lu: School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China
Yihao Xue: School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China
Jiajian Liang: School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China
Yikai Dong: School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China

Mathematics, 2021, vol. 9, issue 22, 1-19

Abstract: 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.

Keywords: adaptive alternating positive and negative feedback; adaptive control; feedback control; catastrophe theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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