Seminar

Abstract:

Synchronization via Funnel Coupling With Application for Decentralized Optimization

Some recent results concerning synchronization of multi-agent systems with a so-called funnel coupling approach are presented. An interesting application is a novel approach to solve an optimization problem in a distributed way. The cost function to be minimized is a sum of local cost functions which are not necessarily convex as long as their sum is convex. Our approach is based on the recent observation that, with a large gain in the diffusive coupling, heterogeneous multi-agent systems behave like a single dynamical system whose vector field is simply the average of all agents' vector fields. However, the design of the large coupling gain requires global information such as network structure and individual agent dynamics. Here, we employ a nonlinear time-varying coupling of diffusive type, which we call edge-wise funnel coupling.

This idea is borrowed from adaptive control, which enables decentralized design of distributed optimizers without knowledge of global information. Remarkably, without a common internal model, each agent achieves asymptotic consensus to the optimal solution of the global cost. We illustrate this result by a network that asymptotically finds the least-squares solution of a linear equation in a distributed manner.