Adaptive synchronization of uncertain dynamical networks with delayed coupling

Abstract

We propose a simple scheme for the synchronization of an uncertain complex dynamical network with delayed coupling. Based on the Lyapunov stability theory of functional differential equations, certain controllers can be designed for ensuring the states of uncertain dynamical network with coupling delays to globally asymptotically synchronize by combining the adaptive method and linear feedback with the updated feedback strength. Different update gains η i will lead to different rates toward synchrony, the choice of which depends on the concrete systems and network models. This strategy can be applied to any complex dynamical network (regular, smallworld, scale-free or random). Numerical examples

Periodically intermittent controlling for finite-time synchronization of complex dynamical networks

“…In inequalities (36) and (37), the control gain is required to be large enough [η ≥ ϑ + cγλ max (A) − ξ max(P ) ], but it may be much large than the needed value. So, some previous works adopted adaptive control approach [14][15], but here we can choose a parameter ξ to adjust the appropriate control gain η.…”

“…Up to now, the synchronization for nonlinear systems especially dynamical networks [12][13] has been widely studied, and many control schemes, such as adaptive control [14][15], pinning control [10,16], observer based control [17], integral control [18], and hybrid feedback control [19], have been focused on this topic. The above effective control approaches are continuous control.…”

Finite-time synchronization of drive-response systems via periodically intermittent adaptive control

“…Many effective control methods including adaptive control [8][9][10][11][12][13][14], feedback control [15][16][17][18], observer control [19][20], pinning control [21][22][23], impulsive control [24][25][26][27][28] and intermittent control [29][30][31][32][33][34][35][36][37] have been proposed to drive the network to achieve synchronization. Among these control approaches, the discontinuous control methods which include impulsive control and intermittent control have attracted much interest due to its practical and easy implementation in engineering fields.…”

Exponential Outer Synchronization between Two Uncertain Time-Varying Complex Networks with Nonlinear Coupling

“…Especially, synchronization of small-world networks, scale-free networks and tree-like networks were investigated in [14][15][16]. In [17], an adaptive feedback scheme was proposed to stabilize the synchronous solution of uncertain complex dynamical network with delayed coupling. Furthermore, the synchronization of networks with partial-information coupling were studied in [18,19].…”