Research On Consensus Problem Of Multi-agent Systems Based On Predictive Mechanisms

With the development of artificial intelligence technologies represented by robots and drones,the problem of coordination and control of multi-agent systems has received more and more attention from control theory scholars.As one of the research hotspots in the field of multi-agent coordination control,consensus problem refers to the fact that all the agents' states reach a same value asymptotically by the communication between local information.For the discrete multi-agent systems,the convergence speed and sampling period are the focus of discussion in the study of consensus problem.How to increase the system's convergence speed and the sampling period threshold to reduce energy loss by paying less communication cost is a meaningful issue.In this paper,we use the theories of graph,algebra,matrix theory and predictive control to study the problems of the discrete multi-agent systems based on the predictive mechanism.By assuming that all the agents possess the predictive intelligence,it is able to increase the convergence speed and extend the sampling period for the system under the premise of realizing the consensus object.At the same time,The equivalent solutions based on MPC(Model Predictive Control)reduce the amount of calculation,have less adjusted parameters and lower memory consumption,which can better meet the real-time requirements in the industrial environment and improve the practical application value of the consensus protocol.The main contents of this paper are as follows:(1)For the consensus problem of the first-order homogeneous discrete-time multi-agent system based on predictive mechanism,an improved MPC-based protocol is designed according to the classic protocol.Numerical simulations demonstrate the effectiveness and advantages of the improved protocol,morever,we point out the main disadvantages of MPC optimal solution based on gradient descent method.(2)Considering the disadvantages of MPC optimal solution based on gradient descent method,the inverse matrix is not conducive to consensus analysis.The iterative equivalent solution of MPC optimal solution is obtained by using algebra and matrix theory,and a sufficient and necessary consensus condition and the upper bound of the sampling period are given.Besides,the principle of the selection for the protocol parameters and the influences of the parameters on the convergence rate of the system are analyzed,and the Lyapunov function of the distributed multi-agent system is given at the same time.(3)For the consensus problem of the second-order homogeneous discrete-time multi-agent system based on predictive mechanism.According to the state feedback second-order consensus protocol,a dynamic consensus protocol including predictive terms is designed,and the traditional MPC solution based on gradient descent method and its equivalent solution are given respectively.Furthermore,a sufficient and necessary consensus condition of the second-order system is obtain by using matrix eigenvalue analysis method,and the influences of the parameters on the convergence property of the system are analyzed.(4)Taking the consensus problem of the heterogeneous discrete-time multi-agent system with time delays based on predictive compensation method into consideration.According to the feedback delays and unobservable input states of the system,a time-delay state observer is first constructed and the output delay is processed by the method of predictive compensation.Then,the consensus protocol is designed based on the predictive values of the observer and the output biases,translating the output consensus problem into the asymptotic stability of closed-loop system.Finally,the controller gains are adjusted through the pole configuration method so that all the eigenvalues of the closed-loop system lie within the unit circle,and a necessary and sufficient consensus condition independent on the delays is also obtained.