Partition-based multi-agent optimization in the presence of lossy and asynchronous communication

Abstract We address the problem of multi-agent partition-based convex optimization which arises, for example, in robot localization problems and in regional state estimation in smart grids. More specifically, the global cost function is the sum of locally coupled cost functions that depend only on each agent variables and their neighbors’ variables. Inspired by a generalized gradient descent strategy, namely the Block Jacobi iteration, we propose an algorithm amenable to a scalable distributed implementation, i.e., each agent eventually computes only the optimal values for its own variables via local communication with its neighbors. In particular, we provide sufficient conditions for global and semi-global exponential stability for the proposed algorithms even in the presence of lossy communications and asynchronous updates. The theoretical analysis relies on novel tools on Lyapunov theory based on separation of time scales and averaging theory for discrete-time systems. Finally, the proposed algorithm is numerically tested on the IEEE 123 nodes distribution feeder in the context of multi-area robust state estimation of smart grids in the presence of measurement outliers.