Modeling and Inverse Complex Generalized Synchronization and Parameter Identification of Non-Identical Nonlinear Complex Systems Using Adaptive Integral Sliding Mode Control

Humaira Afzal,Qarab Raza Butt,Sami Ud Din,Muhammad Rafiq Mufti,Dost Muhammad Khan,Muhammad Imran Qureshi,Waqar Aslam

doi:10.1109/access.2020.2974863

Abstract

This paper presents the Inverse Complex Generalized Synchronization (ICGS) of non-identical nonlinear complex systems with unknown parameters. Using the philosophy of adaptive integral sliding mode control, an adaptive controller and laws regarding parametric upgradation are designed to realize ICGS and parameter identification of two non-identical chaotic complex systems with respect to a given complex map vector. To employ the control, the error system is transformed into a unique structure containing a nominal part and some unknown terms, which are computed adaptively. Then, the error system is stabilized by using integral sliding mode control. The stabilizing controller for the error system is constructed, which consists of the fractional-order control plus some compensator control. To avoid the chattering phenomenon, smooth continuous compensator control is incorporated instead of traditional discontinuous control. The compensator controller and the adapted law are derived in such a way that the time derivative of a Lyapunov function becomes strictly negative. This scheme is applied to synchronize a Memristor-Based Hyperchaotic Complex (MBHC) Lu system and a Memristor-Based Chaotic Complex (MBCC) Lorenz system, a chaotic complex Chen system and a memristor-based chaotic complex Lorenz system with entirely unknown parameters. The effectiveness and feasibility of the proposed scheme is validated through computer simulation using MATLAB software package.

Highlights

Synchronization is a fundamental phenomenon that enables coherent behavior in coupled systems
SOME PRELIMINARIES AND DEFINITION OF Inverse Complex Generalized Synchronization (ICGS) The non-identical drive and response for a complex system with uncertain parameters are represented in the following form: x = F1 (x) + F2 (x) θ
Definition 2: Consider the systems (1) and (2) and at a given map φ (y) : Cm → Cn, ICGS is realized if there exists a controller u (x, y) ∈ C such that lim x − φ (y) = 0 (4)

Summary

INTRODUCTION

Synchronization is a fundamental phenomenon that enables coherent behavior in coupled systems. In [31], [32], the same scheme was employed to synchronize complex systems having a different dimension with uncertain parameters. Via this approach, the slave system could be asymptotically synchronized up to a non-identical or identical master system through a desired complex scaling matrix, and all of the unknown parameters in both systems were estimated by using complex update laws. In our proposed work, the ICGS and parameter estimation scheme is devised by employing adaptive integral sliding mode control, which ensures robustness from the very beginning due to the absence of reaching phase, suppress chattering, ensure finite-time convergence via Lyapunov theory [37]–[39].

SOME PRELIMINARIES AND DEFINITION OF ICGS

EXAMPLE 1

CONCLUSION