Localized Learning of Robust Controllers for Networked Systems with Dynamic Topology

Our previous work proposed an approach to localized adaptive and robust control over a large-scale network of systems subject to a single topological modification. In this paper, we develop this approach into an iterative scheme to handle multiple topological modifications over time, which switch between configurations in a finite-state Markov chain. Each system in the network uses its local information to robustly control its own state while also learning the current state of the network topology (i.e. which state of the Markov chain it is currently in). Additionally, each system maintains an estimate of certain parameters for the overall network, for instance, the transition probabilities of the Markov chain, and each system uses standard average consensus methods to update its estimate. We simulate a simple centered hexagon network with 7 systems and 4 different topological states, and show that each system in the network manages to stabilize under a control law that uses only local information, and adapts to the current topology within a reasonable amount of time after a switch is made.