NDLI: Sampled-data control of coupled harmonic oscillators using measured position states only

Content Provider	IET Digital Library
Author	Zhang, Hua Ji, Jinchen Wu, Quanjun
Abstract	This brief study investigates the synchronisation of undirected coupled harmonic oscillators by using a sampled-data control strategy. In the absence of measured velocity information, each of the networked oscillators can only obtain the measurements of the position states relative to its neighbours at the sampling moments. A distributed protocol based on the sampled relative position measurements at a series of time instants is proposed for the coupled harmonic oscillators. Necessary and sufficient conditions for achieving synchronisation are analytically established in virtue of the graph theory, matrix analysis theory and Schur stability theory of cubic polynomials. Theoretical results indicate that the explicit range that contains all the desirable sampling periods is uniquely determined by the largest eigenvalue of the Laplacian matrix associated with the network graph and the position gain of the harmonic oscillators. An effective simple iterative method is then developed to calculate the range in which the desirable sampling periods fall. Finally, numerical simulations are performed to illustrate the correctness of the theoretical results and effectiveness of the proposed protocol.
Starting Page	985
Ending Page	991
Page Count	7
ISSN	17518644
Volume Number	12
e-ISSN	17518652
Issue Number	Issue 7, May (2018)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-cta/12/7
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-cta.2017.1232
Journal	IET Control Theory & Applications
Publisher Date	2018-01-12
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Combinatorial Mathematics Desirable Sampling Periods Differential Equation (numerical Analysis) Discrete Control System Distributed Protocol Graph Theory Harmonic Oscillator Interpolation And Function Approximation Iterative Method Laplace Equation Laplacian Matrix Linear Algebra Matrix Algebra Matrix Analysis Theory Measured Position State Measured Velocity Information Network Graph Networked Oscillator Numerical Analysis Polynomial Sampled Data System Sampled-data Control Strategy Sampling Moments Schur Stability Theory Time Instants Undirected Coupled Harmonic Oscillator
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Human-Computer Interaction Electrical and Electronic Engineering Computer Science Applications

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