Global finite-time synchronization of different dimensional chaotic systems

Abstract

This paper addresses the problem of global finite-time synchronization of two different dimensional chaotic systems. Firstly, the definition of global finite-time synchronization of different dimensional chaotic systems are introduced. Based on the finitetime stability methods, the controller is designed such that the chaotic systems are globally synchronized in a finite time. Then, some uncertain parameters are adopted in the chaotic systems, new control law and dynamical parameter estimation are proposed to guarantee that the global finite-time synchronization can be obtained. By considering a dynamical parameter designed in the controller, the adaptive updated controller is also designed to achieve the desired results. At last, the results of two different dimensional chaotic systems are also extended to two different dimensional networked chaotic systems. Finally, three numerical examples are given to verify the validity of the proposed methods.

Dynamical Analysis and Stabilization of Wind Turbine Drivetrain via Adaptive Fixed‐Time Terminal Sliding Mode Controller

“…Lemma 4 (see [19]). Based on Lemma 3, if = 1, the continuous positive definite and radially unbounded function ( ( )) can be written as follows:…”

“…Mathematical Problems in Engineering where , > 0, 1 > > 0; it meets ( ) ≡ 0, ∀ > T 2 max .The convergence time T 2 max is given by T 2 max = 0 + (1/(1− ) )In(( + 1− ( 0 ))/ ). Lemma 5 (see [19]). From Lemma 4, when = 0, ∀ ≥ 0 , the global finite time should be rewritten as T 3 max = 0 + 1− ( 0 )/(1 − ) , and 2 ≤ 3 for ( 0 ) ≥ 0.…”

“…The effective control of uncertain nonlinear dynamic systems has been a hot issue of academia. The various advanced control methods including feedback control [17], fuzzy control [18], adaptive control [19], and sliding mode control [20] have been studied to drive the dynamic system to the expected orbit or achieve these synchronization problems. Among these control strategies, the stability and secure operation of dynamic systems with uncertainties can all be guaranteed.…”

Adaptive Second-Order Sliding Mode Algorithm-Based Modified Function Projective Synchronization of Uncertain Hyperchaotic Systems

“…The fast convergence, high accuracy, robustness, and disturbance rejection ability are the demonstrated characteristics of the FTC [18]. Therefore, the FTC techniquebased synchronization has been received an increasing attention in recent years [19]- [25]. Although only few FTC works are partially considering some sub-classes of MFPS in the current literature, they can be readily applied to a general MFPS problem after relevant modification.…”

“…Wang et al [24] introduced an adaptive FTC for synchronizing uncertain Lorenz-Stenflo systems; however, their results only ensure the finite-time stability with special initial conditions related to the Lyapunov function candidate, which is hardly satisfied. On the basis of the finite-time stability theory, Zhang et al [25] proposed a modified adaptive FTC strategy aimed at achieving the global FTSY of different dimensional chaotic systems. However, some of priori-unknown parameters are required to implement the update laws in Eqs.…”