The Research On The Resource Allocation Problem Of Multi-Agent Systems Based On The Event-Triggered Communication

With the extensive research on the wireless sensor networks,large-scale smart grids,and formation control,the distributed resource allocation problem abstracted in these systems has attracted more and more scholars' attention,in which the sensors are connected by a communication network.However,in the actual system,there are characteristics such as a poor communication environment and scattered nodes.To ensure the control characteristics of the system and the efficient use of limited communication bandwidth,based on the Lagrangian multiplier method,this paper designs a distributed optimization algorithm with event-triggered communication mechanism.We can summarize the research work of this paper in the following three points:As for the distributed quadratic resource allocation problem over an undirected continuoustime system,this paper designs a static and dynamic event-triggered distributed optimization algorithm for obtaining the optimal solution while realizing lower communication consumption.In the static event-triggered controller,the sum of the squares of the state differences of the neighboring Lagrangian multipliers is used as the threshold of the trigger.In the dynamic event-triggered controller,a dynamic variable is designed to ensure the existence of the positive lower bound of the inter-event time.For the distributed convex resource allocation problem over an undirected continuoustime system,this paper proposes an event-triggered distributed optimization algorithm with discrete-time communication.The differential equation of the Lagrangian multiplier is established by using the classical PI control.The auxiliary variable accumulates the historical information of Lagrangian multipliers and balances the difference between the actual state and the virtual state of the agent.This paper proposes a fast convergence algorithm by establishing a static mapping relationship between Lagrange multipliers and node state values.To avoid the inverse operation of the gradient of the aim function,this paper establishes another algorithm by using the sub-gradient and Lagrangian multiplier information,in which the agent state values are obtained through differential equations.The agent state is fixed within the constraint range by the mapping method.Finally,the convergence and effectiveness of the two algorithms are proved and verified through theoretical analysis and case studies,respectively.For the distributed resource allocation problem in an unbalanced directed network,this paper proposes a surplus-based and subgradient-based algorithm for solving the quadratic and convex resource allocation problem,respectively.To reduce communication consumption,the event-triggered communication mechanism is considered.besides,in which an exponential term is added to the threshold.Finally,case simulations verify the effectiveness of the two discrete-time event-triggered algorithms.