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

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 finitetime/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 timevarying 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.