The Analysis And Optimization Of Networked Harmonic Oscillators' Coordinated Dynamics

Coupled oscillators network is an important model to study the coordinated behavior and collective dynamics of the self-organized systems in the natural world and human society.This model can well describe the self-organized structures and the dynamics characteristics of many physical or biological systems,such as neural networks,genetic control networks,protein networks,social networks and electric power networks.In this literature,coupled harmonic oscillators system has become an extremely typical model in the fields of the classical physics and the quantum physics in recent years and has important scientific significance and potential applications due to its typical physical structures and abundant intrinsic dynamics.In this paper,from the perspectives of the dynamics and control,we consider the coupled harmonic oscillators which only has relative position coupling in a series of discrete time.A distributed input control protocol is designed based on the delayed sampled relative position states.This system can achieve complete synchronization only by the delayed sampled relative position states in a series of discrete time,rather than sampled relative velocity states.By the stability theory and the matrix analysis theory,an exact function relationship about the sampling interval,the time-delays and the oscillators frequency is obtained as a sufficient and necessary condition for the synchronization.Numerical simulations further verify the correctness of the theoretical results and the effectiveness of the input control protocol.In addition,for the optimized control of networked harmonic oscillators system,a performance index which characterizes the least energy consumption of the system is designed by considering energy consumption factors.An input control sequence is further optimized to make the system achieve its minimal energy consumption.