Design Of Multi-agent Distributed Optimization Algorithms Over Directed Switching Topologies

In recent years,distributed optimization algorithms for multi-agent systems have received increasing attention due to their wide applications in sensor networks,robot networks,machine learning and other fields.Distributed optimization algorithms distribute the computing tasks to each node to improve processing efficiency,and have the high performance of improving processing efficiency,protecting data privacy and improving system robustness.In practical multiagent system networks,different agents often transmit information at different power level,and the communication line may have limitations.These often lead to unidirectional communication between the agents,and make the communication topology graphs directional.Due to actual needs or external interference,communication network is likely to change due to actual needs or external interference,which can lead to system instability.Therefore,the study of distributed optimization algorithms over switching topologies has high actual application value.This paper investigates the design of distributed optimization algorithm over directed switching topologies,and the specific works are listed as follows:For the distributed optimization problem of multi-agent systems with time-varying communication topologies,a distributed optimization algorithm is proposed,in which the output states of the agents achieve consensus and reach the global optimal value point by exchanging local cost functions gradient and state information between their neighbors.Specifically,considering that the system state derivatives at the switching point may be discontinuous,the differential inclusion expression is used to model the switching system as a hybrid system for analysis.The average dwell-time and time-ratio constraint are utilized to constrain the switching law which limits the switching frequency of the communication topologies and the dwell-time of different communication topologies.Finally,stability analysis is given by using Lyapunov stability theory,and the effectiveness of the proposed algorithm is verified by a numerical simulation.For the resource allocation problem of multi-agent systems under time-varying communication topologies,a distributed resource allocation algorithm is proposed.Firstly,considering only the supply-demand balance equation constraint,the resource allocation goal with the minimized economic cost is achieved by combining the micro-increment technique.Secondly,the inequality constraints of the agents are further considered,and the optimal solution to the resource allocation problem is obtained by introducing auxiliary variables and correcting the result which only considers only the supply-demand balance constraint.The stability of the algorithm is proved by using Lyapunov stability theory,and the corresponding exponential convergence rate is given.Finally,taking a power scheduling problem for instance,the effectiveness of the proposed algorithm is verified by simulation.