Design Of Distributed Predictive Controller For Linear Multi-Agent System

Model Predictive Control(MPC),which can deal with all kinds of system constraints explicitly online,has attracted the attention of many scholars since its birth.However,the emergence of Multi-Agent System(MAS)with complex system structure and diverse control objectives makes it difficult for traditional centralized MPC algorithm to solve the control problems among agents that can communicate,then Distributed Model Predictive Control(DMPC)was generated.Since the local information between the agents was utilized by DMPC algorithm to achieve the optimal performance of the whole system,therefore,a lot of DMPC research results of MAS have emerged,but there are still some issues to be resolved.Therefore,aiming at the problems existing in multi-agent system,such as heavy burden of communication between agents,the controller design is more conservative and the amount of online calculation is relatively large,a novel DMPC algorithm is designed.The main research contents include the following aspects:(1)A DMPC algorithm based on error upper bound is proposed for a class of linear multi-agent systems with constrained coupling to alleviate the communication burden between agents.Firstly,based on the local state error of adjacent agents,an index function that needs to solve "min-max" is introduced to construct a neighborhood error upper bound condition to determine whether the state information of agents needs to be transmitted to neighboring agents,which can reduce the communication burden between agents.Then,according to the established error upper bound condition,an improved coupling constraint is constructed so that the states in the terminal constraint set also satisfy this constraint,furthermore,the optimal controller is obtained by solving the DMPC optimization problem including terminal cost,terminal constraint set,terminal controller and constraints.Finally,simulation results demonstrate the effectiveness of the proposed algorithm.(2)A DMPC algorithm with time-varying terminal constraints is proposed for a class of multi-agent systems with coupled state and control inputs.First of all,the coupling effect of adjacent agents is regarded as a bounded disturbance to introduce a nominal system model corresponding to the agent system,and a performance index function containing only nominal system variables is further designed to ensure the global optimal system performance and reduce the online computation of DMPC.Then,a novel time-varying terminal constraint set design method is presented under the framework of DMPC,and a predictive controller is designed by solving the DMPC optimization problem under constraints.Finally,simulation results demonstrate the effectiveness of the proposed algorithm.(3)A robust DMPC design method is proposed for a class of uncertain multi-agent systems with parallel structures.According to the complexity of the actual system,the uncertain multi-agent system is considered as follows: the competitive coupling and competitive constraint in parallel structure system are defined based on the characteristics of parallel structure,and the infinite time domain "min-max" optimization problem of robust DMPC is transformed into a finite time domain optimization problem that contains linear matrix inequality(LMI)constraints by using the LMI method,then an explicit feedback control law expression is designed for each agent.Finally,simulation results demonstrate the effectiveness of the proposed algorithm.