Improved Distributed Optimization Algorithm for Continuous Time Multi-agent Systems With Time-Varying Cost Function

This paper mainly discusses the improved distributed optimization problem for first-order multi-agent system with time-varying cost function. The goal of this paper is to make all agent's states reach agreement in finite time and to minimize the global objective function. Each agent is individual and only corresponds to a gradient information. Firstly, we improve the existing distributed optimization algorithm with time-varying cost function. Secondly, by constructing some new Lyapunov functions and using the methods of convex analysis, sufficient conditions for all agents to reach consensus and to be derived to optimal solution are given, where the optimal solution is a trajectory that changes over time. Finally, Some numerical simulation examples are given to verify the effectiveness of the theoretical results.