Distributed Optimization Based On Multi-Agent System Consistency

In recent years,distributed optimization problems based on multi-agent systems have attracted widespread attention due to their extensive applications in the fields of science and engineering.In particular,the design of optimization algorithms and the analysis of their convergence are one of the frontier topics in the field of optimization research.Based on the consistency of nonlinear multi-agent system,this paper discusses the distributed optimization problem and the optimal control problem of fractional order linear multi-agent system.The main research contents are as follows:Firstly,for the absolutely continuous functions,a novel principle of predefined-time convergence is proposed.For nonlinear multi-agent systems,a finite time observer is designed to solve the distributed dynamic optimization problem with equality constraints in predefined-time by using non-smooth analysis methods and differential inclusion techniques.Secondly,for the absolutely continuous functions,a new principle of predefined-time convergence is proposed.For nonlinear multi-agent systems,using the Lyapunov function method,inequality lemma,and the proposed predefined-time lemma,the predefined-time consensus conditions are derived in terms of multi-agent systems.Solve distributed optimization problems with equality constraints.Finally,for fractional order linear multi-agent system,a control protocol with adaptive and constant edge dependent synchronization gains is designed,and an adaptive control strategy is applied to obtain sufficient conditions for multi-agent system to reach stabilization.Based on the proposed cost function,provide the corresponding optimal control design scheme.Distributed optimization has a wide practical background.Therefore,the research on distributed optimization problems based on the unity of multiple intelligent systems has high value both in theory and in practical engineering.