Distributed Optimization And Control Problem Based On Multi-agent Consensus

Multi-agent system is a system composed of interconnected subsystems or agents.The basic idea is to implement a distributed control protocol for each agent and use the information interaction of neighboring agents to complete the collective tasks of the entire system.Largescale multi-agent systems have attracted much attention in industry and academia due to their synergy,high efficiency,scalability and other advantages.Distributed optimization refers to a group of interconnected agents using local information to minimize a common objective function.It has important research significance and application value in large-scale numerical computing,sensor networks,cyber-physical systems,etc.Multi-agent system is the implementation carrier of distributed optimization,the consensus problem,convergence problem,and dynamic problem in multi-agent systems have gradually become one of the research hotspots in the field of distributed optimization and control.In the view of the research contents and objectives of the distributed optimization and control problems in the above-mentioned multi-agent system,this paper focuses on the hybrid consensus distributed optimization algorithm containing node errors,the second-order distributed consensus optimization algorithm based on the quasi-Newton method,and the distribution under malicious node attacks.The problem of dynamic consensus of the formula is studied,and the main contents and conclusions are as follows:1.A hybrid communication distributed optimization algorithm with node errors is proposed.By studying the basic model and iterative update expression of distributed optimization algorithm based on hybrid communication graph,a distributed alternating direction method of multiplier algorithm with node error is proposed to solve the problem of additive node error in network communication.Under the condition that the obj ective function satisfies the strong convexity and the gradient function satisfies the Lipschitz continuity,the analytical upper and lower bounds of the mean square steady-state error are analyzed,and the linear convergence of the algorithm is verified by Q-linear convergence.Finally,by setting different disturbance errors,the influence of the network connectivity rate and the number of effective nodes in the network on the performance of the algorithm is tested,and it is fully verified that the proposed algorithm can accelerate the distributed and consensus alternating direction method of multiplier algorithm with node errors.2.A distributed optimization algorithm based on a weighted hybrid communication graph is proposed.In order to accelerate the convergence speed of hybrid communication distributed optimization algorithm containing node errors,through in-depth analysis of the internal structure of the underlying network communication topology,the edge weight of the super edge in the hybrid communication graph is considered,and a distributed a distributed alternating direction method of multiplier optimization algorithm based on the weighted hybrid communication graph is proposed,and the iterative update expression of the original variable and the dual variable is introduced.Using the Douglas-Rachford splitting algorithm,when the objective function satisfies strong convexity and smoothness,and the gradient function satisfies the Lipschitz continuity condition,the linear convergence of the algorithm is verified and the analytical upper and lower bounds of the mean square steady-state error are analyzed.Finally,the weight matrix in the mixed constraint is generated through the center of the edge betweenness,and the acceleration performance of the algorithm is verified by the Erdos-Renyi random network based on two types of cluster graphs.3.A second-order distributed alternating direction method of multiplier optimization algorithm based on the quasi-Newton method is proposed.Aiming at the problem of low convergence accuracy of the first-order optimization algorithm,we study the basic model of the second-order quasi newton algorithm and the iterative update formula,analyze the cause of irreversibility of the Hessian matrix,and propose the inverse matrix of Hessian matrix in the quasi-newton algorithm by the parameter correction method.The fully distributed quasi-Newton method is used to approximate an internal optimization problem,and the distributed dual quasiNewton update method is used to accelerate the dual ascent process relative to the dual gradient iteration.When the objective function satisfies the assumptions of strong convexity,smoothness and second-order differentiability,and the eigenvalues of the Hessian matrix and its inverse matrix are bounded,the linear convergence of the algorithm is analyzed.Finally,the algorithm is applied to a type of ellipse fitting problem,using the fitting error and the average absolute percentage error to compare with the existing algorithms,and comparing the convergence speed,iteration time,and convergence accuracy to verify the effectiveness of the algorithm.4.The consensus problem of linear multi-agent system under malicious node attack is proposed.Aiming at consensus problem when there are unstable factors such as node failures and malicious attacks in the network system,based on the directed acyclic network topology,a controller with evaluation correction function is designed,and a resistance based on neighboring node monitoring and isolation is proposed.The malicious node interference algorithm identifies malicious nodes by accumulating the reputation value of neighboring nodes,and monitors their status in real time.In order to reduce the influence of malicious deviation on the system,a correction function based on state deviation is designed to modify the controller,a correction algorithm based on state deviation of malicious nodes is proposed,and the convergence proof is given by Lyapunov theorem.Finally,numerical simulation experiments and a six-degree-offreedom UAV formation system verify the effectiveness of the algorithm.5.A linear multi-agent system model predictive control based on a hybrid communication graph is proposed.Aiming at the problem that the network system cannot converge due to malicious deviations when the fusion center in the linear multi-agent system is attacked by malicious nodes,using the good performance of the hybrid communication graph,the distributed model predictive control is combined with the hybrid consensus alternating direction method of multiplier algorithm,and a hybrid consensus model predictive control algorithm based on the hybrid communication graph is proposed.A reasonable confidence interval is set through reputation values to identify,isolate the malicious nodes.A control strategy based on the Byzantine protocol is designed to correct the malicious nodes.In order to effectively solve the periodic oscillation of the system caused by malicious deviation,a hybrid consensus model predictive control algorithm with adaptive correction based on historical state is proposed.Finally,when the objective function satisfies the strong convexity and the gradient function satisfies the Lipschitz continuous condition,the upper and lower bounds of the system mean square steadystate error are analyzed,and the effectiveness of the algorithm is verified by numerical simulation experiments.In a word,based on the study of the topology of the hybrid communication network,this paper proposes a distributed ADMM algorithm with node errors in the hybrid communication graph,revealing the influence of the edge weight of the hyper-edge on the convergence performance of the algorithm;a second-order distribution is designed.The optimized algorithm achieves the improvement of convergence accuracy and convergence speed;a control strategy based on neighboring node monitoring and isolation is proposed,which realizes the consensus coordinated control of the network system under the attack of malicious nodes.The above research and conclusions have important theoretical guidance and practical significance for distributed optimization and control problems based on multi-agent consensus.