Differential Quadrature Method For Dynamics Of Multi-agent Distributed Parameter System

With the development of network communication technology,computer technology,and sensor network,multi-agent systems are widely used in various fields such as aerospace,deep-sea exploration,and robot simulation training.The traditional lumped parameter model cannot reasonably solve the problems of lack of important parameters,excessive error,and difficult analysis of convergence.Distributed parameter models are often presented as relatively complex partial differential equations,and the state space described is infinite-dimensional.The state variables and control variables are not only functions of time,but also include changes in spatial coordinates.Traditional numerical methods are difficult to solve.This thesis mainly studies the differential quadrature method of dynamic simulation calculation for the multi-agent system under the distributed parameter system.In the differential quadrature method,the derivative values of the discrete points in the equation are approximated by the weighted sum of the function values of each point in the solution domain,and the discrete solution is performed.Its mathematical principle is simple,and only a small number of nodes are needed to obtain better data accuracy.This thesis first gives the explicit expression of the coefficient matrix of the differential quadrature method under the Lagrangian interpolation basis function and the trigonometric interpolation basis function,then analyzes several commonly used methods for dealing with boundary conditions,and gives an applicable Lagrangian multiplier method for dealing with boundary conditions of multi-agent distributed parameter systems.Then take the multi-agent distributed parameter system under two typical control methods based on Lyapunov method control and iterative learning control as an example to carry out numerical simulation,establish the differential quadrature formula of the system state equation,and study the differential quadrature method in typical control methods The performance in the second-order and fourth-order systems,and analyze the influence of different parameters such as the number of nodes,node distribution,and step size on the multi-agent distributed parameter system.The simulation results show that the differential quadrature method can be quickly and effectively simulated after selecting appropriate parameters.Using the above conclusions,the differential quadrature method is applied to the active vibration suppression system of the flexible beam.The simulation results of the example show that the multi-agent distributed parameter system meets the design expectations of the control law,and further demonstrates that the differential quadrature method is applied to the multi-agent system.The reliability and feasibility of the agent distributed parameter system,the application of this method contributes to the development of multi-agent control science.