PhD ceremony Mr. S. Zhang: Analyzing network dynamics through graph partitioning

PhD ceremony: Mr. S. Zhang

Dissertation: Analyzing network dynamics through graph partitioning

Promotor(s): prof. M.K. Camlibel, prof. M. Cao, prof. J.M.A. Scherpen

Faculty: Mathematics and Natural Sciences

In this thesis, we study problems for diffusively coupled networks: controllability, partial consensus and disturbance decoupling problem. To study controllability of networks, we introduce diffusively coupled networks with general linear dynamical agents, some of which receive external command signals and are called leaders. Then we reveal the role that linear dynamics of agents and the network topology play in controllability of the overall network. After that, we turn to networks consisting of single-integrator agents, for which we provide both the upper bounds and the lower bounds of the controllable subspace in terms of distance partitions and almost equitable partitions of the underlying graphs of the networks. Following that, we investigate networks which have distance regular topologies and provide a strategy to choose leaders to render networks to be controllable. Most of the above results are extended to the case when networks switch arbitrarily within a finite set of admissible topologies.

To investigate partial consensus problem, we consider heterogeneous diffusively coupled networks with double-integrator agents. We provide both the algebraic necessary and sufficient conditions as well as the graph theoretical necessary conditions for achieving partial consensus.

As for the disturbance decoupling problem, we focus on diffusively coupled networks with single-integrator agents, some of which receive external disturbance signals. In particular, we develop the so-called almost equitable partitions with respect to a given cell, in terms of which we provide a graph theoretical sufficient condition to solve the disturbance decoupling problem for networks.