Coordinated Control Of Harmonic Oscillators With Communication And Input Delays

In recent years, distributed coordinated control of networked multi-agent sys-tems has attracted increasing attention from various fields of science and engineer-ing. Among them, the synchronization and control of coupled harmonic oscillators, which is viewed as a fundamental model for the study of coordination problems of networked multi-agent systems, has been a significant topic in both theoretical research and practical applications due to its intrinsic dynamics properties and po-tential applications, including the control of multiple robots, formation control of unmanned aerial vehicle, mobile sensor networks. This dissertation is mainly con-cerned with complete synchronization and group synchronization issues of coupled harmonic oscillators with communication and input delays through discontinuous control strategy. In details, the main contents of this dissertation are summarized as follows:1. Synchronization of instantaneous coupled harmonic oscillators with commu-nication and input delays. By virtue of impulsive control strategy, a synchronization algorithm with communication and input delays is proposed for coupled harmonic oscillator systems. Furthermore, some general and algebraic criteria on convergence are established for such algorithm. The effects of communication and input delays on synchronization performance of coupled harmonic oscillators are discussed under undirected topology. It is shown that the communication delays have more impor-tant impact than the input delays on determining synchronization dynamics of coupled harmonic oscillators. Explicitly, in absence of communication delays, cou-pled harmonic oscillators can achieve synchronization oscillatory motion, whereas so long as communication delays are nonzero, its synchronization state is zero. In addition, as for instantaneous coupled harmonic oscillators only with input delays, synchronization criteria are also brought forward.2. Sampled-data synchronization of coupled harmonic oscillators with, commu-nication and input delays subject to controller failure. Some algebraic criteria on convergence for directed coupled harmonic oscillators are established by combin-ing sampled-data control and intermittent control technique. The main features include:(i) both communication delays and input delays are simultaneously ad- dressed in the case of the directed network topology; (ii) the effects of time delays on synchronization performance are theoretically and numerically investigated. In addition, numerical simulations show that increasing either communication or input delays will enhance the synchronization performance of coupled harmonic oscilla-tors.3. Group synchronization of diffusively directed coupled harmonic oscillators with nonidentical and identical agent dynamics. Group synchronization issues of diffusively directed coupled harmonic oscillators are discussed for nonidentical and identical agent dynamics. For the case of coupled nonidentical harmonic oscillators with positive coupling, group synchronization can always be achieved for coupled harmonic oscillators under strongly connected topology. When topology is acyclic partition, the group synchronization states are some periodic orbits with the same frequency and are simply related with the initial values of certain group regardless of ones of the other groups. For the case of coupled identical harmonic oscilla-tors with positive and negative coupling, some generic algebraic criteria on group synchronization with continuous and discontinuous interaction are established respectively.