Distributed Optimization Algorithm for Discrete-Time Heterogeneous Multi-Agent Systems With Nonuniform Stepsizes

This paper is devoted to the distributed optimization problem of heterogeneous multi-agent systems, where the communication topology is jointly strongly connected and the dynamics of each agent is the first-order or second-order integrator. A new distributed algorithm is first designed for each agent based on the local objective function and the local neighbors' information that each agent can access. By a model transformation, the original closed-loop system is converted into a time-varying system and the system matrix of which is a stochastic matrix at any time. Then, by the properties of the stochastic matrix, it is proven that all agents' position states can converge to the optimal solution of a team objective function provided the union communication topology is strongly connected. Finally, the simulation results are provided to verify the effectiveness of the distributed algorithm proposed in this paper.