Dynamical adaptive synchronization

Abstract

The notions of dynamical synchronization and adaptive dynamical synchronization problems are introduced. The algorithm solving adaptive synchronization problem for a subclass of Lurie systems with exciting input is proposed. The performance and potentialities of proposed solutions are demonstrated by two examples related to formation control and self-organization of swarm systems.

Passive control of n-dimensional chaotic complex nonlinear systems

“…In the literature, since the chaos control problem was considered by Ott et al (1990), many valuable control methods have been developed to control chaotic systems, such as impulsive control (Chen et al 2004), adaptive control (Efimov 2006), sliding mode control (Chiang et al 2007), fuzzy control (Yau and Shieh 2007), optimal control (Tian and Yu 2000), digital redesign control (Guo et al 2000), backstepping control (Zhang et al 2004), and many others. The concept of passivity of nonlinear systems has aroused new interest in the nonlinear control field (Willems 1972;Vidyasagar 1979;Byrnes et al 1991;Calcev 1998;Pogromsky 1998;Xie et al 1998;Chua 1999;Wen 1999;Lou and Cui 2007;Wang and Liu 2007a,b;Wei and Luo 2008;Xiang-Jun et al 2008;Budiyono et al 2009;Kemih 2009;Chen and Liu 2010;Sangpet and Kuntanapreeda 2010a,b;Wei et al 2010).…”

Robust chaos synchronization of four-dimensional energy resource systems subject to unmatched uncertainties

“…There is much prospect of chaos synchronization being applied in the vast areas of physics and engineering systems such as in power converters, chemical reactions, biological systems, information processing, especially in secure communication where a lot of progress has been achieved [2][3][4][5][6]. Nowadays, different techniques and methods have been proposed to achieve chaos synchronization such as adaptive control [7][8][9][10][11], sliding mode control (SMC) [12][13][14], impulsive control [15,16], linear control [17], optimal control [18], digital redesign control [19], and backstepping control [20,21].…”

Exponential synchronization of chaotic systems subject to uncertainties in the control input

“…Chaos synchronization can be applied in the vast areas of physics and engineering science, especially in secure communication [2][3][4]. Recently, many control methods have been developed to achieve chaos synchronization between two chaotic systems with different initial conditions, such as adaptive control [5][6][7][8], linear balanced feedback control [9], impulsive control [10,11], sliding mode control [12][13][14], fuzzy control [15], backstepping control [16][17][18], and so on. However, the implementation of control inputs of practical systems is frequently subject to uncertainties as a result of physical limitations.…”