Adaptive Distributed Convex Optimization For Mulit-agent Svstems

These years have witnessed a growing research interest in multi-agents systems,such as consensus control,distributed formation control,distributed optimization,etc.Due to its wide use in wireless sensor network,smart power grids,machine learning and so on,distributed optimization has been extensively studied.This article studies a general distributed convex optimization problem for a linear multi-agent system.The global objective function of the multi-agent system is strictly convex,and is defined by the sum of the local objective functions which only associated with each agents.The ob-jective of the agents are to collectively minimize the global objective function.We provide an adaptive protocol to solve the distributed convex optimization problem and show that using the provided protocol,the agents can converge to a common state value which simultaneously optimizes the global objective function.It is worth mentioning that the control gains in the proposed protocol are designed in an adaptive way such that the global information on the objective functions and the network topology is not needed anymore.Moreover,we study the implementation of the protocol with discrete-time communication and provide an upper bound on the time interval that guarantees the convergence of the protocol.Then,two numerical examples are provided to veri-fy the above-mentioned results.In addition,we consider the perturbation term in the dynamics of the agents which could result from disturbances,uncertainties and mod-eling errors,etc.We propose a neural-network-based protocol for distributed convex optimization to eliminate the influence of the perturbation term in the dynamics.It is shown that using the neural-network-based protocol,the consensus and optimization of the agents will not be affected by the perturbation term.