Dynamics And Control In Hybrid Networked Harmonic Oscillator Systems

Networked harmonic oscillator system is usually regarded as a fundamental mod-el in complex systems and complex dynamical networks, and has attracted many re-searchers from various disciplines of dynamics and control in complex systems. Fur-thermore, it has important applications in many engineering felds such as cooperativemulti-robots systems, mobile sensor networks, intelligent transmission systems and soon due to its representative physics and mechanical characteristic. As a result, the co-ordinated behavior and cooperative control of networked harmonic oscillators is of bothgreat scientifc signifcance and wide variety of applications. This dissertation is mainlyconcerned with the issues of synchronization and control in hybrid networked harmonicoscillator from the view of dynamics and control. In details, the fundamental contribu-tions of these works are summarized in the following four aspects:1. Synchronization of networked harmonic oscillators under local instantaneous in-teraction. A distributed synchronization algorithm in undirected networks of net-worked harmonic oscillators systems under local instantaneous interaction is p-resented. The convergence analysis for such algorithm over fxed and switchingundirected network topologies with and without communication delays is providedrespectively. Some convergence conditions by which the coupled harmonic oscil-lators achieve synchronized oscillatory motions under instantaneous network con-nectivity are established analytically. Diferent from the existing pure continuousor discrete-time algorithms, a distinctive feature of this work is to solve synchro-nization problem in undirected networks even if each oscillator instantaneously ex-changes the information of the velocity with its neighbors only at some discretemoments.2. Synchronization of sampled-data coupled harmonic oscillators with control input-s missing. In view of the technological appeal of digital implementations as wellas a wide variety of network environments factors, a distributed sampled-data al-gorithm with controller failures for synchronization of coupled harmonic oscilla-tors in undirected networks is presented. Based on the theory of discontinuousdynamical systems, a new method for the convergence analysis of the algorithms isproposed, and then some generic synchronization criteria for such algorithm over,respectively, undirected fxed and switching network topologies with and withoutcommunication delays are derived analytically. In addition, the relationship amongthe ‘work-time’,‘rest-time’ and the time delay in addition with its efects on theconvergence rate are also discussed.3. Distributed impulsive consensus for second-order multi-agent systems with com-munication delays. A distributed consensus protocol for second-order multi-agentsystems having communications time delays is proposed. It is assumed that each agent can only exchange the position information with its neighbors at a series ofdiscrete time instants and update its velocity state in the form of abrupt jumps set-ting. A distinctive feature of this algorithm is to address consensus problems forsecond-order multi-agent systems with local instantaneous interaction. It is shownthat convergence can be exponentially reached if the interaction graph of the sys-tem is connected and the interaction interval is less than a given threshold value.In particular, the convergence rate does not depend on the network topology butdepend on the parameter of the agent’s dynamics and the coupling interval undersome restrictive condition when their is no communication time delays, which isdiferent from most existing results in the literature.4. Synchronization in complex delayed dynamical networks with impulsive coupling.A general model of complex delayed dynamical networks with impulsive couplingis established. By using the impulsive control theory in delayed dynamical sys-tems, some simple yet generic criteria for global and local synchronization of suchdynamical networks are derived analytically. It turns out that the coupled delayeddynamical networks can always achieve synchronization even there are connectionsamong the nodes only at some discrete moments. Furthermore, the results are ap-plied to the problem of synchronization of typical nearest neighboring coupled SFnetworks consisting of the chaotic delayed Hopfeld neural networks and chaoticFHN neuron oscillators.