Model Predictive Control Based Consensus Scheme Of Discrete Multi-agent Systems

In this paper,the consensus problem of discrete-time multi-agent systems based on Model Predictive Control(MPC)is studied.The consensus problem is how to design a consensus protocol so that the states or outputs of all agents tend to be the same.The consensus of MAS has been paid much attention recently.In this paper,discrete multi-agent systems with fixed topology and communication delay are considered respectively,and some studies on these two types of systems are carried out by using MPC strategy,as follows:The state consensus of MPC for discrete-time multi-agent systems with communication delays is considered.When there is delay in the process of information transmission between adjacent agents,the control protocol design method of multi-agent system without delay can not deal with this situation.Therefore,a new control protocol design method is needed.Based on the extremum principle and mathematical induction,a distributed MPC state consensus protocol is presented.In order to facilitate discussion,a new graph is constructed,and the relationship between the new topology graph and the original topology graph is given through a lemma.By using the error between the agent and the neighbor agent and constructing the Lyapunov-Krasovskii function,a MPC cost function with terminal constraint is monotonically decreasing,and the conditions for achieving state consensus of discrete multi-agent system with communication delay are given.For the general linear discrete-time multi-agent system,the output consensus problem is discussed based MPC strategy.Since the output may not be affected by all states,the output consensus problem becomes more complicated.By introducing two subspaces of the output space,and using two linear transformations and partial stability theory,the conditions for achieving output consensus of discrete multi-agent system are given.By designing the terminal weighting matrix in the performance index function,the performance index function decreases monotonically,and a sufficient condition for the output to be consistent is obtained.Then,by using LMI method and projection theorem,the optimal solution of the optimization problem is obtained,and the output consensus protocol based on MPC strategy is designed.