Distributed Continuous-time Optimization over Second-order Multi-agent Networks with Nonuniform Gains

This paper mainly focuses on the distributed optimization problem over second-order multi-agent networks, where the team objective function is the sum of some local differentiable convex functions. Assume one local objective function can only be known by one agent. Based on the local neighbors’ information, a new distributed optimization algorithm with nonuniform gains is proposed. By a new coordination transformation, the closed-loop system can be decomposed into two one-order system. It is proved that all agents can reach an agreement and the team objective function can be minimized by analyzing these two one-order systems. Finally, a simulation example ia given to show the effectiveness of the theoretical results.