Adaptive impulsive synchronization of a class of chaotic and hyperchaotic systems

Abstract

In this paper, the issue of synchronization and parameter identification for a class of chaotic and hyperchaotic systems is discussed. Based on the theories of adaptive control and impulsive control, a synchronization scheme is developed to achieve complete synchronization and parameter identification of a class of chaotic and hyperchaotic systems for the first time. Sufficient conditions are derived to synchronize the systems with different impulse distances. The bounds of the stable regions are also estimated. Numerical examples are presented to demonstrate the effectiveness of the proposed controllers and identifiers.

Complex function projective synchronization of general networked chaotic systems by using complex adaptive fuzzy logic

“…Synchronization of coupled chaotic systems is one of typical collective behaviors in complex networked systems due to its practical applications such as biological neural networks and communication security [10,11]. Several types of synchronization have been investigated [12][13][14][15][16][17][18][19][20][21][22][23]. For example, by using the adaptiveimpulsive control, the complete synchronization for a class of chaotic and hyperchaotic systems is investigated [14].…”

“…Several types of synchronization have been investigated [12][13][14][15][16][17][18][19][20][21][22][23]. For example, by using the adaptiveimpulsive control, the complete synchronization for a class of chaotic and hyperchaotic systems is investigated [14]. Tracking control and generalized projective synchronization for a class of hyperchaotic system is investigated by the adaptive control scheme [15].…”

Further results on the impulsive synchronization of uncertain complex‐variable chaotic delayed systems

“…What is more important, impulsive control allows synchronization between chaotic systems only by small impulses being sent to the received systems at the discrete impulsive instances and which can reduce the information redundancy in the transmitted signal and increase robustness against the disturbances. Recently, impulsive control and synchronization of real-variable chaotic systems have been deeply studied, and many valuable results have been obtained [12,13,16]. Impulsive synchronization of uncertain real-variable chaotic systems is studied via adaptive strategy, which can relax the restrictions on the impulsive interval [12,16], and the references therein.…”

Adaptive impulsive synchronization of uncertain delayed chaotic system with full unknown parameters via discrete‐time drive signals

“…Unfortunately, due to the complexity and uncertainty of chaotic system, it is not always feasible to obtain the knowledge of parameters in some practical cases. In recent years, there has been an increasing interest in adaptive impulsive synchronization of chaotic systems with unknown parameters [6,[22][23][24][25]. In these methods, the parameters adaptive laws are designed using the continuous output of drive systems.…”

“…In these methods, the parameters adaptive laws are designed using the continuous output of drive systems. For example, in [14] and [22], the vector y(t) 5 Cx(t) and g(x(t)) are used to construct the parameters adaptive laws, respectively, where x(t) is the continuous output of the drive system. In [23][24][25], the parameters adaptive laws are designed using the synchronization error variable e i (t) 5 y i (t) 2 x i (t), where x i (t) is the continuous signal of the drive system.…”