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.
Highlights
In the process of actual control, the control target and its environment are very complex, and its parameters are changed by various internal and external factors
According to the phenomenon in which some system state changes in the actual material system often exist from quantitative change to qualitative change or from a stable stage to another stable stage, Yan proposed some elements of the multi-scale positive and negative feedback alternation theory [8], and described the action state mathematically, according to the dynamic evolution rule of the idea, which achieved good results in the task of nonlinear time series prediction [9]
Can we find a control strategy to make the system switch between different states adaptively when it is working to obtain the advantages of negative feedback and positive feedback? Inspired by the aforementioned challenges, we focus on an APNF control model with excellent characteristics of both positive and negative feedback
Summary
In the process of actual control, the control target and its environment are very complex, and its parameters are changed by various internal and external factors. According to the phenomenon in which some system state changes in the actual material system often exist from quantitative change to qualitative change or from a stable stage to another stable stage, Yan proposed some elements of the multi-scale positive and negative feedback alternation theory [8], and described the action state mathematically, according to the dynamic evolution rule of the idea, which achieved good results in the task of nonlinear time series prediction [9] These studies show that it is feasible to use mutation to adjust the system state to achieve the desired dynamic behavior
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