Stabilization of Port Hamiltonian Chaotic Systems with Hidden Attractors by Adaptive Terminal Sliding Mode Control.

Ahmad Taher Azar,Fernando E Serrano

doi:10.3390/e22010122

Abstract

In this study, the design of an adaptive terminal sliding mode controller for the stabilization of port Hamiltonian chaotic systems with hidden attractors is proposed. This study begins with the design methodology of a chaotic oscillator with a hidden attractor implementing the topological framework for its respective design. With this technique it is possible to design a 2-D chaotic oscillator, which is then converted into port-Hamiltonia to track and analyze these models for the stabilization of the hidden chaotic attractors created by this analysis. Adaptive terminal sliding mode controllers (ATSMC) are built when a Hamiltonian system has a chaotic behavior and a hidden attractor is detected. A Lyapunov approach is used to formulate the adaptive device controller by creating a control law and the adaptive law, which are used online to make the system states stable while at the same time suppressing its chaotic behavior. The empirical tests obtaining the discussion and conclusions of this thesis should verify the theoretical findings.

Highlights

Chaos theory represents a new field of research based on qualitative and empirical analysis of chaotic a periodic behavior [1,2,3,4,5,6,7]
Self-excited attractors are those kind in which the domain of attraction is at least one of the equilibrium points, whereas hidden attractors are those whereas the domain of attraction is not balanced [12]
Chaotic system with hidden attractor is designed and analyzed in which the eigenvalues and Lyapunov exponents are obtained for dynamical analysis purposes

Summary

Introduction

Chaos theory represents a new field of research based on qualitative and empirical analysis of chaotic a periodic behavior [1,2,3,4,5,6,7]. Chaotic systems with hidden attractors have been extensively studied during recent years because the vast amount of physical systems in which this phenomenon is found [8,9,10,11]. In the literature there are many studies in which hidden attractors are analyzed, for example, in [13], a new 3-D chaotic system with hidden attractor is designed and analyzed in which the eigenvalues and Lyapunov exponents are obtained for dynamical analysis purposes. Other examples can be found in [14], in which a simple 4-D chaotic system is evinced in the presence of a hyperbolic cosine nonlinearity, where some phenomenons such as multistability, antimonotonicity, and quasi-periodic orbits are analyzed

Methods

Discussion

Conclusion