Research And Application Of A Class Of Distributed Optimization Algorithm

In recent years,with the rapid development of information technology,the distributed optimization algorithm for multi-agent system has attracted extensive attention because of its broad application prospects,such as unmanned aerial vehicles formation control,wireless sensor network,machine learning,deep learning and so on.The distributed optimization is based on the consensus algorithm to reach consensus and simultaneously minimize the global objective function through exchanging informations.The finite-time optimization with timevarying objective function and distributed optimization and consensus problem and application for heterogeneous multi-agent system in noisy environment are mainly investigated.The main research contents are as follows:1.The distributed finite-time optimization problem with time-varying cost function is investigated.Firstly,the existing distributed finite-time optimization algorithms are summarized in this paper,a novel first-order optimization algorithm is proposed.Secondly,assuming that the local objective functions are convex,and the gradients is bounded,it is proved that the algorithm can drive all agent to find the optimal solution of the global objective function by using only local gradient information.Finally,the simulation examples are given to verify the correctness of the theoretical analysis,and the simulation example of existing algorithm is given to compare the advantages and disadvantages of the algorithms.2.For undirected connected topology,distributed time-varying optimization problem for second-order multi-agent system with state constrains is investigated.Different from existing distributed optimization algorithm,this paper assumes that the objective function is time-varying and quadratic differentiable convex function.Besides,this paper is not required that the Hessian matrices are identical and the gradients are bounded.Firstly,the existing distributed time-varying optimization algorithms are summarized,a new second-order distributed control protocol with state constraints is proposed.Furthermore,by convex analysis and Lyapunov stability theory,it is proved that the states of all agents can reach consensus,asymptotically converge to the neighborhood of the optimal point of the global objective function,and this range is adjusted by the control gain.Finally,the simulation examples are given to verify the correctness of the theoretical analysis.3.The consensus and distributed optimization problem of discrete-time heterogeneous multi-agent system in noisy environment is investigated.To weak the effects of noise,the step-size rule of stochastic approximation is introduced,a novel distributed control protocol is designed.On the one hand,for consensus problem with communication noises,when the topology is strongly connected digraph,the sufficient conditions are given for the states of all agents to reach consensus almost surely； when the topology is balanced digraph,the sufficient conditions are given for the system states to converge to a random variable with bounded variances,and its’ expectation is related to the initial states of agents.However,in practical engineering application,there may be errors between the control gain of agents and the designed ones.To solve this problem,the consensus algorithm with agent-dependent control gain is designed.The sufficient conditions are given for the states of all agents to reach consensus and converge to a random variable almost surely,respectively.On the other hand,for distributed optimization problem with communication noises and sub-gradient noises,Firstly,to weak the effects of communication noises and sub-gradient noises,two step-size rules of stochastic approximation are introduced.Secondly,by a model transformation,the original closed-loop system is changed into an equivalent time-varying system.Furthermore,by using Lyapunov stability theory and stochastic analysis,the convergence of system is analyzed.For joint strongly connected digraph,it is proved that the position states of all agent can almost surely converge to the optimal point of the global objective function,and the velocities of all second-order almost surely converge to zero.Finally,the simulation example is given to verify the correctness of the theoretical analysis,and the application of the algorithm in regression analysis is discussed.