The Consensus Of Coupled Harmonic Oscillators

In recent years,multi-agent systems play an important role in applications,including communication network,biological sciences,coordinated control of unmanned aerial vehicles(UAVs),distributed sensor networks control,robots formation.Coordination of multi-agent systems of control has attracted increasingly attention from various fields of experts and scholars.Consensus is ones of the most important issue in coordination control,which means all the agents reach an agreement regarding a certain physical quantity.In physics and electrical engineering,harmonic oscillator is an important model.Interconnected harmonic oscillators combine a network of coupled harmonic oscillators.Consensus of coupled harmonic oscillators has become focus a research object.In this paper,consensus question of coupled harmonic oscillators is considered.Reasonable and effective control protocols are introduced for coupled harmonic oscillators.The main contents are summarized as follows.Firstly,the consensus of coupled harmonic oscillators with bounded disturbance is investigated.Consensus protocol is proposed by using the variable structure control method and sufficient conditions are obtained for realizing consensus.Convergence analysis is given based on Lyapunov stability theory,LaSalle Invariance Principle,algebraic graph theory and matrix theory.Finally,numerical simulation is used to verify the validity of the proposed protocol.Secondly,the consensus of coupled harmonic oscillators without velocity measurements is studied.The control protocol for consensus of coupled harmonic oscillators is proposed without velocity measurements,without with a leader,respectively.With the aid of algebraic graph theory,Lyapunov stability theory,and other related knowledge,some sufficient conditions of network consensus are obtained.Finally,numerical simulation is used to verify the validity of the proposed protocol.Thirdly,adaptive consensus of coupled harmonic oscillators is considered.Aiming at the consensus of couple harmonic oscillators,distributed adaptive control protocol is designed.By applying thealgebraic graph theory,matrix theory,Lyapunov stability theory,LaSalle Invariance Principle,the sufficient condition on consensus of the network is obtained,and convergence analysis is provided.Finally,numerical simulation is used to verify the validity of the proposed protocol.