Distributed adaptive control of pinning synchronization in complex dynamical networks with non-delayed and delayed coupling

Abstract

This paper discusses the distributed adaptive control schemes for pinning synchronization in complex dynamical network with non-delayed and delayed coupling. An effective distributed adaptive strategy to adjust simultaneously coupling strength and feedback gains is designed based on information of the non-delayed network's configuration. For a special case where the information of delay is available, a distributed adaptive scheme to tune the coupling weights of non-delayed coupling network is proposed by using the delayed feedback controllers. Based on the small-world network and scalefree network, simulation examples are given to demonstrate the effectiveness of theoretical analysis.

Pinning synchronization of nonlinear hybrid‐coupled complex networks with double time delays via aperiodically intermittent adaptive control

“…The coming is the estimation of (t) on the basis of above Equations (7) and (8). When 0 = t 0 ≤ t ≤ s 0 , from Lemma 1, one has (t) ≤(t 0 )e − (t−t 0 ) ,…”

“…[1][2][3] Some complex dynamical networks can synchronize by themselves, but others should be forced to synchronize by adding external controllers. Thus, a lot of control methods such as linear or nonlinear feedback control, [4][5][6][7] adaptive control, [8][9][10][11][12] and sliding-mode control [13][14][15] have been studied extensively and deeply by researchers in various disciplines. Accordingly, these control methods can be continuous, [4][5][6][7][8][9][10][11][12][13][14][15] impulsive, [16][17][18][19] or intermittent [20][21][22][23][24][25][26][27][28][29][30][31][32] during the acquisition of complex network synchronization.…”

“…Thus, a lot of control methods such as linear or nonlinear feedback control, 4‐7 adaptive control, 8‐12 and sliding‐mode control 13‐15 have been studied extensively and deeply by researchers in various disciplines. Accordingly, these control methods can be continuous, 4‐15 impulsive, 16‐19 or intermittent 20‐32 during the acquisition of complex network synchronization. Different from other control strategies, intermittent control is active in some time intervals and dormant in others, which shows that it has the feature of economy.…”

Pinning Synchronization for Complex Networks with Interval Coupling Delay by Variable Subintervals Method and Finsler’s Lemma

“…In [16], by using piecewise Lyapunov theory, some less conservative criteria are deduced for exponential synchronization of the complex networks. In [17], a new adaptive intermittent scheme is used to deduce some novel criteria by utilizing a piecewise auxiliary and other relative references [18][19][20][21]. However, in the above papers, many useful situations such as some novel delay processing methods and Finsler's Lemma which can introduce more matrix-valued coefficients to synchronization criteria are not utilized.…”

“…Then more matrix-valued coefficients can be introduced to reduce conservatism. Moreover, our methods can also be applied to most of the existing synchronization results, such as [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”