Research On Distributed Constrained Optimization Of Multi-Agent Systems

As general and information technology continue to advance,optimization problems in large-scale complex network environments have garnered increasing attention.Traditional centralized methods for addressing such problems are becoming increasingly costly and inefficient,with poor stability and weak interference rejection capabilities,making them prone to failure.To overcome these limitations,researchers have proposed distributed optimization algorithms.Unlike centralized optimization algorithms,distributed optimization algorithms do not require a central node.Instead,they decompose complex large-scale optimization problems in network systems into smaller,more manageable sub-problems.The goal of distributed optimization is for multiple agents to cooperate in finding the optimal solution while only having access to their own information and information obtained through interactions with neighboring agents.The algorithm minimizes the sum of the agents’ local objective functions.In practice,an agent’s local objective function or constraints may change over time,causing the optimal solution to the optimization problem to vary accordingly.Additionally,real-world optimization problems are often subject to various constraints.This thesis focuses on scenarios where the objective function and constraints are time-varying and investigates distributed optimization in multi-agent systems.The main contributions include:(1)The distributed optimization in second-order multi-agent systems where the objective functions and inequality constraints are time-varying is studied.Specifically,a distributed optimization problem with time-varying equality constraints is transformed into a distributed time-varying unconstrained optimization problem using the Lagrange multiplier method.We then design a distributed optimization algorithm with time-varying adaptive control gain based on the consistency condition and KKT condition.Additionally,the increase of time-varying adaptive control gains enables agents to achieve consistency.The asymptotic convergence of the proposed algorithm is demonstrated making use of Lyapunov stability theory.Finally,the effectiveness of the algorithm is demonstrated through MATLAB simulations.(2)The distributed finite-time optimization in first-order multi-agent systems where the objective functions and inequality constraints are time-varying is studied.A distributed optimization problem with time-varying inequality constraints is transformed into a distributed time-varying unconstrained optimization problem via the use of the logarithmic barrier penalty function method.We then can design a distributed finite-time optimization algorithm based on the finite-time consistency condition and distributed average tracking method.The algorithm estimates global gradient information and global Hessian matrix information for the required agents using local information,relaxing the assumption that all agents’ Hessian matrices are equal.Moreover,we demonstrate finite-time convergence of the proposed algorithm using the Lyapunov framework of finite-time stability.Finally,the effectiveness of the proposed algorithm is demonstrated through numerical simulations.