Research On Multi-agent Distributed Optimization Algorithm Considering Constraint

In recent years,with the development of artificial intelligence and the communications industry,multi-agent systems have been widely applied in various aspects of life.As a fundamental problem in multi-agent systems,distributed optimization has attracted significant attention from numerous researchers.Optimization methods based on distributed architectures transform complex problems into multiple local optimization problems.Agents only need to communicate with their neighboring agents and obtain local optimal solutions through multiple iterations,thereby achieving global optimality for the entire system.The paper employs algebraic graph theory for multi-agent systems,Lyapunov stability analysis methods,cooperative optimization techniques,and other related theories to address convex optimization problems with equality and inequality constraints.We propose a distributed optimization algorithm considering constraints to solve convex optimization problems in multi-agent systems.The main research content includes the following three aspects:(1)For quadratic convex optimization problems in multi-agent systems with equality constraints,we design a distributed dynamic event-triggered optimization algorithm based on periodic sampling information.The algorithm uses periodic sampling information for eventtriggered condition design and provides algorithm stability conditions related to the sampling period.This effectively avoids the continuous detection problem of event-triggered conditions and the Zeno phenomenon,better aligning with the actual system operation mechanism.Compared with traditional static event-triggered conditions,the designed dynamic eventtriggered conditions have a lower triggering frequency,effectively reducing communication and controller update frequency among agents.(2)For distributed optimization problems with equality constraints,we consider the case where the communication topology graph among agents is directed and propose an asynchronous distributed optimization algorithm.The algorithm’s convergence analysis is conducted using matrix brake theory and Lyapunov stability methods,and the necessary and sufficient conditions for algorithm stability are given.The algorithm can solve quadratic optimization problems in multi-agent systems with directed communication topology.(3)For distributed optimization problems with multiple constraints,this paper uses an adaptive adjustment mechanism to adaptively adjust the cost function parameters of agents and designs their adaptive adjustment law.Furthermore,a distributed optimization algorithm is established to directly solve quadratic optimization problems with equality and inequality constraints.The designed algorithm is applied to the economic dispatch problem in microgrids,verifying its effectiveness.