Effect of Delay on Cooperative Control Schemes

Abstract:

In this talk we will investigate what effect heterogeneous feedback delays can have on the operation of a range of cooperative control schemes - consensus, rendezvous, flocking and synchronization. We will consider various models corresponding to different delay types (e.g., communication or self-delay) and we will propose controllers that lead to scalable (i.e., independent of the size of the network) robustness - either in a delay-dependent or delay-independent fashion. We will consider models that are either linear, nonlinear with relative degree one and integrating behavior, or a class of nonlinear models with relative degree two. In some cases, the graph structure will be restricted to be undirected whereas in other cases, we will allow switching topologies. We will also concentrate on performance measures and develop a method for estimating the rate of convergence for such schemes when delays are present.