Infinite-time and finite-time synchronization of coupled harmonic oscillators

Abstract

This paper studies the infinite-time and finite-time synchronization of coupled harmonic oscillators with distributed protocol in the scenarios with and without a leader. In the absence of a leader, the convergence conditions and the final trajectories that each harmonic oscillator follows are developed. In the presence of a leader, it is shown that all harmonic oscillators can achieve the trajectory of the leader in finite time. Numerical simulations of six coupled harmonic oscillators are given to show the effects of the interaction function parameter, algebraic connectivity and initial conditions on the convergence time.

Group synchronization of diffusively coupled harmonic oscillators

“…[2,7,8,11]. In particular, remarkable effort has been devoted to the synchronization and control of coupled harmonic oscillators [1,3,15,18,19,27,29], in part because it plays a significant role in various engineering applications of coupled multi-agent systems involving cooperative behaviors including mapping, sampling, patrol or surveillance [1,15,18]. As a consequence, a large quantity of synchronization protocols (or algorithms) have recently been proposed for coupled harmonic oscillators from various perspectives.…”

“…Moreover, Su et al addressed the same issue in a dynamic proximity network without any network connectivity assumption [18]. In addition, Cheng et al [3] focused on the infinite-time and finite-time synchronization of coupled harmonic oscillators with the external disturbance. More recently, Zhou et al also studied the impulsive or sampled-data synchronization of coupled harmonic oscillators based on some discontinuous or hybrid control schemes [27,29].…”

Sampled-data synchronisation of coupled harmonic oscillators with communication and input delays subject to controller failure

“…Finally, it plays a significant role in various applications of multi-agent systems involving cooperative behaviours including mapping, sampling, patrol or surveillance (Ballard, Cao, & Ren, 2010;Ren, 2008;Su, Wang, & Lin, 2009). As a consequence, a large quantity of synchronisation protocols (or algorithms) have recently been proposed and analysed for coupled harmonic oscillators from various perspectives (see Ballard et al, 2010;Cheng, Ji, & Zhou, 2011;Ren, 2008;Su et al, 2009;Zhang, Zhou, & Liu, 2012;Zhou, Zhang, Xiang, & Wu, 2012 and references cited therein).…”

Sampled-data synchronization of coupled harmonic oscillators with controller failure and communication delays

“…3 As a consequence, a large amount of synchronization protocols (or algorithms) have recently been presented for coupled harmonic oscillators from various perspectives. [1][2][3][4][5][6][7][8] In a recent paper, Ren 1 investigated the synchronization problem of n coupled harmonic oscillators connected by the dampers, where the dynamics of each oscillator is given bẏ…”

“…Ballard et al 3 further focused on this issue in the framework of discrete-time setting, and a distributed protocol is proposed to implement synchronized motion coordination of multiple mobile robots. In addition, Cheng et al 5 addressed the finite-time and infinite-time synchronization of networked harmonic oscillators with the external disturbance. Very recently, Zhang et al 6,8 also taken into account the distributed synchronization problem of coupled harmonic oscillators under local instantaneous or impulsive interactions and sampled-data information with control inputs missing.…”