Consensus dynamics in distribution networks and nonlinear multi-agent systems

In this thesis we first consider a basic model of a dynamical distribution network, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and outflows. In order to achieve the output agreement among the vertices, we employ distributed PI controllers which regulate the flow inputs. Then we consider the flow constraint and storage constraint cases respectively. For the flow constraint case, we derive sufficient and necessary conditions for output agreement, which only depend on the structure of the network and the flow constraint intervals. For the storage constraint case, we design a PI controller with state-based saturation for the flows to achieve the output agreement and to keep the storage constraint being satisfied all the time.Second we study consensus problems for multi-agent systems defined on directed graphs where the consensus dynamics involves nonlinear and discontinuous functions. Sufficient (and necessary in some cases) conditions, involving the nonlinear functions and the topology of the underlying graph, for the agents to converge to static consensus are provided. For a special case, namely the multi-agent system defined on a strongly connected graph with continuous functions, we show the convergence by using a port-Hamiltonian formulation