Extended Exploration Grey Wolf Optimization, CFOA-Based Circuit Implementation of the sigr Function and its Applications in Finite-Time Terminal Sliding Mode Control

Abstract

The development of closed-loop circuit realizations of chaotic synchronization and control is considered a promising aspect of analog electronics. Therefore, this paper explores the use of the <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sigr</monospace> function in the implementation of finite-time terminal sliding mode control. A CFOA-based implementation of the <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sigr</monospace> function is proposed, whereby an Extended Exploration Grey Wolf Optimization method is used to approximate the non-integer powered transfer function inside the <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sigr</monospace> function. This configuration also allows for a parallel configuration in which each coefficient of the transfer function can be independently and elaborately tuned. Two closed-loop circuit realizations of second- and third-order systems are presented to demonstrate the effectiveness of the developed <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sigr</monospace> function to achieve finite-time terminal sliding mode control. For the second-order system, the terminal sliding mode control is applied to stabilize the chaos in the Holmes-Duffing system in finite time, and for the third-order system, active stabilization of the modified Sprott-C chaotic system is presented. The results show that finite-time control has been satisfactorily achieved in both cases, both in computer simulations and in circuit implementations. Specifically, the second-order closed-loop circuit implementation yielded a maximum error of 1.11%, while the third-order closed-loop circuit implementation had a maximum error of 2.89%.