Optimum PID Control of Multi-wing Attractors in A Family of Lorenz-like Chaotic Systems

TL;DR

This paper presents a genetic algorithm-based method for designing optimal PID controllers to stabilize complex multi-wing Lorenz-like chaotic systems, improving control over their highly unpredictable dynamics.

Contribution

It introduces a novel global optimization framework using real-coded genetic algorithms for PID control of multi-wing chaotic systems.

Findings

Successful stabilization of Lu, Rucklidge, and Sprott-1 systems.

Enhanced control accuracy over multi-wing chaotic attractors.

Demonstrated effectiveness of GA-based optimization in nonlinear chaos control.

Abstract

Multi-wing chaotic attractors are highly complex nonlinear dynamical systems with higher number of index-2 equilibrium points. Due to the presence of several equilibrium points, randomness of the state time series for these multi-wing chaotic systems is higher than that of the conventional double wing chaotic attractors. A real coded Genetic Algorithm (GA) based global optimization framework has been presented in this paper, to design optimum PID controllers so as to control the state trajectories of three different multi-wing Lorenz like chaotic systems viz. Lu, Rucklidge and Sprott-1 system.