Finite-time/fixed-time distributed optimization for nonlinear multi-agent systems with time-varying cost function

Abstract

Distributed optimization, combining cooperative control and optimization objectives, is vital for practical applications. While current research predominantly focuses on linear multi-agent systems, the real-world demands often involve nonlinear systems with finite or fixed time constraints. This paper addresses the finite-time/fixed-time distributed optimization for nonlinear multi-agent systems with time-varying cost function. Under appropriate assumptions, we propose a finite-time distributed protocol and a fixed-time distributed protocol for the nonlinear multi-agent systems to ensure all agents achieve consensus and minimize the time-varying cost function, relaxing the conditions for strong convexity and bounded gradient difference of the cost function. Simulation experiments validate the effectiveness of these distributed protocols.