Robust Distributed Optimization for Multiagent Systems With General Linear Models

Abstract

We propose a general approach to the problem of distributed feedback optimization for both continuous- and discrete-time, linear uncertain multiagent systems. When the agent's dynamics are subject to disturbances and parametric uncertainties, and the gradients of the local objective functions can only be measured through each agent's output, the problem falls outside the scope of traditional distributed optimization algorithms. This article combines an internal-model-based controller with a distributed optimization algorithm to provide a solution that guarantees robust asymptotic stability of the optimal steady state. The analysis is based on Lyapunov theory, on the time-scale separation properties of the considered optimization algorithm, and on the robustness of internal-model-based control.