Optimal targeting of nonlinear chaotic systems using a novel evolutionary computing strategy

TL;DR

This paper introduces a novel metaheuristic called Teaching-learning-based optimization for controlling chaotic systems, demonstrating its effectiveness on well-known models and discussing potential engineering applications.

Contribution

It presents a new population-based optimization method for chaos control, showing its rapid convergence and effectiveness on Henon and Ushio systems.

Findings

Effective in directing chaotic orbits towards targets

Rapid convergence with small perturbations

Potential for engineering chaos control applications

Abstract

Control of chaotic systems to given targets is a subject of substantial and well-developed research issue in nonlinear science, which can be formulated as a class of multi-modal constrained numerical optimization problem with multi-dimensional decision variables. This investigation elucidates the feasibility of applying a novel population-based metaheuristics labelled here as Teaching-learning-based optimization to direct the orbits of discrete chaotic dynamical systems towards the desired target region. Several consecutive control steps of small bounded perturbations are made in the Teaching-learning-based optimization strategy to direct the chaotic series towards the optimal neighborhood of the desired target rapidly, where a conventional controller is effective for chaos control. Working with the dynamics of the well-known Henon as well as Ushio discrete chaotic systems, we assess the effectiveness and efficiency of the Teaching-learning-based optimization based optimal control technique, meanwhile the impacts of the core parameters on performances are also discussed. Furthermore, possible engineering applications of directing chaotic orbits are discussed.