Distributed Optimization in Heterogeneous Dynamical Networks

Abstract

In this paper, distributed optimization in heterogeneous dynamical networks that consist of both single- and double-integrator agents are studied. This paper is divided into two main parts. In the first part, all agents shall reach a consensus point that minimizes the sum of local convex objective functions. In the proposed solution, it is assumed that the local objective functions are only available to their associated agents. These agents have access to the states information of their neighbors through a communication protocol. These agents admit no constraints. In the second part, we will tackle the same distributed optimization problem as the one in the first part; however, we assume that each agent is subject to a local decoupled constraint set. To solve this problem, we will adopt an embedded control scheme in which each agent integrates a virtual unit that cooperates with those of neighboring agents to produce proper reference signals for the original dynamics. These reference signals conduct the agents toward the globally optimal point. Then, we design decentralized feedback controllers to make the agents track the reference signals. Stability analysis and convergence proof are given for the both parts. At the end, we simulate the proposed approaches on a group of heterogeneous wheeled robots.