Distributed Optimization for Two Types of Heterogeneous Multiagent Systems

This article studies distributed optimization algorithms for heterogeneous multiagent systems under an undirected and connected communication graph. Two types of heterogeneities are discussed. First, we consider a class of multiagent systems composed of both continuous-time dynamic agents and discrete-time dynamic agents. The agents coordinate with each other to minimize a global objective function that is the sum of their local convex objective functions. A distributed subgradient method is proposed for each agent in the network. It is proved that driven by the proposed updating law, the agents' position states converge to an optimal solution of the optimization problem, provided that the subgradients of the objective functions are bounded, the step size is not summable but square summable, and the sampling period is bounded by some constant. Second, we consider a class of multiagent systems composed of both first-order dynamic agents and second-order dynamic agents. It is proved that the agents' position states converge to the unique optimal solution if the objective functions are strongly convex, continuously differentiable, and the gradients are globally Lipschitz. Numerical examples are given to verify the conclusions.