On the controllability of networks with nonidentical linear nodes

"The controllability of dynamical networks depends on both network structure and node dynamics. For networks of linearly coupled linear dynamical systems the controllability of the network can be determined using the well-known Kalman rank criterion. In the case of identical nodes the problem can be decomposed in local and structural contributions. However, for strictly different nodes an alternative approach is needed. We decomposed the controllability matrix into a structural component, which only depends on the networks structure and a dynamical component which includes the dynamical description of the nodes in the network. Using this approach we show that controllability of dynamical networks with strictly different linear nodes is dominated by the dynamical component. Therefore even a structurally uncontrollable network of different nn dimensional nodes becomes controllable if the dynamics of its nodes are properly chosen. Conversely, a structurally controllable network becomes uncontrollable for a given choice of the node’s dynamics. Furthermore, as nodes are not identical, we can have nodes that are uncontrollable in isolation, while the entire network is controllable, in this sense the node’s controllability is overwritten by the network even if the structure is uncontrollable. We illustrate our results using single-controller networks and extend our findings to conventional networks with large number of nodes.

Failure Analysis in Multi-Agent Networks: A Graph-Theoretic Approach

A multi-agent network system consists of a group of dynamic control agents which interact according to a given information flow structure. Such cooperative dynamics over a network may be strongly affected by the removal of network nodes and communication links, thus potentially compromising the functionality of the overall system. The chief purpose of this thesis is to explore and address the challenges of multi-agent cooperative control under various fault and failure scenarios by analyzing the network graph-topology. In the first part, the agents are assumed to evolve according to the linear agreement protocol. Link failures in the network are characterized based on the ability to distinguish the agent dynamics before and after failures. Sufficient topological conditions are provided, under which dynamics of a given agent is distinguishable for distinct digraphs. The second part of this thesis is concerned with the preservation of structural controllability for a multi-agent network under simultaneous link and agent failures. To this end, the previously studied concepts of link and agent controllability degrees are first exploited to provide quantitative measures for the contribution of a particular link or agent to the controllability of the overall network. Next, the case when both communication links and agents in the network can fail simultaneously is considered, and graphical conditions for preservation of controllability are investigated