Research On The Cooperative Control Methods Of Multi-agent Systems Based On Time-delay Controllers

Due to the wide existence of time-delay in multi-agent system,and the significance of improving the performance of multi-agent system based on time-delay controller,multiple kinds of time-delay controller are proposed in this paper.Firstly,the design method of single-delay controller for first-order multi-agent system based on Lambert W function is investigated.The multi-agent system is decoupled into several SISO(single-input single-output)subsystem.For a single-integral multi-agent system,heterogeneous controllers for multi-agent system are designed based on Lambert W function.The rightmost pole of each subsystem is chosen within the allowable range.For the general first-order system,a region of the control parameters is obtained.In this range,the parameter values that cause the minimal value of the maximum rightmost poles of the close-loop system can be easily found.According to the performance requirement,appropriate control parameters can be chosen.This method is also applicable to the multi-agent system with directed topology.Secondly,the design method of the distributed H? two-delay controller for arbitrary-order multi-agent system is studied.The region of the control parameters that can stabilize the arbitrary-order SISO system is obtained.Moreover,the control parameters are optimized by H? performance indexes.Furthermore,the problem of designing distributed controllers for the multi-agent system is converted to the one of designing the controllers for subsystems by using matrix theory.Based on the design method of the two-delay controllers for SISO systems,the distributed H? two-delay controller for the multi-agent system is derived.Finally,for more flexibility in adjusting the control parameters,the proportional-integral-delay controller is proposed.For the second-order multi-agent system with strong connected undirected topology,poles placement is implemented based on the proportional-integral-delay controllers.The analytical expressions of the control parameters are obtained with respect to the desired pole based on the method of designing maximum decay rate methodology.For the arbitrary-order multi-agent system with directed topology,the region of the control parameters that can stabilize the system is presented based on D-decomposition method.With the design method of the distributed time-delay controller in this paper,the performance of the multi-agent system is improved based on time-delay.The proposed controllers have the advantages of low order,easy implementation and wide application range.This will provide effective theory for taking advantages of the time-delay in multi-agent system.