Distributed extremum seeking control of multi-agent systems with unknown dynamics for optimal resource allocation

Abstract

The paper considers a class of equality constrained resource allocation problems for dynamically coupled multi-agent systems. It is assumed that the mathematical structure of each agent’s dynamics and its local cost function are unknown but depend on the entire resource allocation vector. A distributed dual-mode extremum seeking control is proposed. It is shown that the distributed approach decouples the local contribution of each agent locally while guaranteeing a solution of the network wide optimization problem subject to the resource allocation constraints. The agents operate over a communication network which enables the application of a dynamic consensus algorithm to generate local estimates of the total network cost. Locally, each agent implements a parameter estimation routine to estimate the gradient of the total cost with respect to the local action. Each agent uses its local gradient estimate to implement a dual mode extremum seeking controller that guarantees satisfaction of the resource allocation constraints. Two simulation examples are provided to demonstrate the effectiveness of the proposed technique.