A nonlinear dynamical system with a large number of states can be viewed as a collection of nonlinear dynamical (sub)systems, with fewer states each, that interact with each other. The interactions among the subsystems can be depicted using a directed graph where each node corresponds to a subsystem and each edge - an interaction between two such subsystems. Owing to the use of graph structure, such systems are called Nonlinear Dynamical Networks (NDNs).
In this talk we address a class of NDNs with identical subsystems (nodes) and time varying interactions (edges). We use the framework of Temporal Networks to represent such NDNs. The aim of analyzing such an NDN is to make it follow a desired system trajectory in finite time (i.e) finite time synchronization. We synchronize a few nodes initially using external control inputs. These nodes are termed as pinning nodes. The other nodes are synchronized by interacting with the pinning nodes and with each other. We derive the sufficient conditions for the network to be synchronized. Next, we formulate an optimization problem to minimize the number of pinning nodes for synchronizing the entire network. Finally, we address the problem of maximizing the number of synchronized nodes when there are constraints on the number of nodes that could be pinned. We show that this problem belongs to the class of NP hard problems and propose a greedy heuristic. We illustrate the results using numerical simulations.