Bounded Partial Pinning Control of Network Dynamical Systems

Controlling collective behavior has been the key goal of researchers both from the engineering and physics communities working in the field of control of network systems. In the literature, pinning control has often emerged as the tool of choice to achieve this task. Only recently though, has the problem of controlling only a fraction of the network nodes been tackled. Here, we consider the case in which, due to the disturbing influence of an external node, which we identify as an opponent, the network nodes cannot asymptotically converge to the pinner's trajectory, and only a bounded convergence can be achieved. We derive analytic conditions guaranteeing that all the nodes in a given strongly connected component of the network achieve bounded convergence to the trajectory of the pinner, and provide an estimate of the convergence bound. Finally, we apply our results to an opinion dynamics scenario, showing that a pinned node selection strategy grounded on our theoretical results is effective in steering the opinions of the majority of the network nodes towards that of the pinner.