In complex networked systems, the structure of the underlying communication between individual agents can have profound impacts on the performance and dynamics of the system as a whole. For example, processes such as consensus can occur at faster or slower rates depending on the structure of the communication graph, and the synchronisation of coupled chaotic oscillators may be unachievable in one conﬁguration, when it is achievable in another. As such, it is vital for agents within a complex networked system to be able to make estimates of the properties of the network as a whole, and be able to direct their own actions to modify these properties in a desirable way, even when they are only able to communicate with their direct neighbours, and have no global knowledge of the structure of the network. In this thesis we explore decentralised strategies by which individual agents in a network can make estimates of several functions of the graph Laplacian matrix eigenvalues, and control or optimise these functions in a desired manner, subject to constraints. We focus on the following spectral functions of the graph Laplacian matrix, which determine or bound many interesting properties of graphs and dynamics on networks: the algebraic connectivity (the smallest nonzero eigenvalue), the spectral radius (the largest eigenvalue), the ratio between these extremal eigenvalues (also known as the synchronisability ratio), the total effective graph resistance (proportional to the sum of the reciprocals of nonzero eigenvalues), and the reduced determinant (the product of the nonzero eigenvalues).
Date of Award  20 Mar 2018 

Original language  English 

Awarding Institution   The University of Bristol


Supervisor  Mario Di Bernardo (Supervisor) & Guido Herrmann (Supervisor) 

 Distributed optimisation
 Graph Laplacian
 Complex networks
Distributed Control and Optimisation of Complex Networks via their Laplacian Spectra
Kempton, L. (Author). 20 Mar 2018
Student thesis: Doctoral Thesis › Doctor of Philosophy (PhD)