Distributed Model Predictive Control Of Multi-agent Systems

In the practical applications, the complex systems have the features of complex model,large scale, a great amount of variables and constraints. However, the traditional control methods cannot satisfy the requirements of the complex systems. Over the past years,distributed model predictive control(DMPC) is becoming an important tool to handle the large-scale complex systems due to its good control performance, capability of handling constraints and the structural flexibility. In the embryonic stage, the research of DMPC is confronted with many difficulties. For example, how to deal with the couplings between subsystems in order to make the optimization problem of each subsystem solvable; how to design the terminal ingredients(terminal cost, terminal controller and positive invariant terminal set) for each subsystem; how to guarantee the recursive feasibility and the closedloop stability of the whole system.Motivated by this, this dissertation focuses on the research of DMPC for multi-agent systems and explores the problems of regulation, consensus and formation, respectively.The main contents and results in this dissertation are summarized as follows:1. A DMPC algorithm is presented for the regulation of linear multi-agent systems with the coupled cost and coupled constraints. At each sampling time, all the agents are permitted to synchronously optimise. An improved compatibility constraint is constructed to ensure the consistency between the actual state trajectory of each agent and its assumed one. With the parameters of the coupled constraints, a positive invariant terminal set, which can definitely ensure the satisfaction of the coupled constraint, and an associated terminal cost(a local Lyapunov function) are designed in a distributed manner. By applying the proposed distributed optimization algorithm, the recursive feasibility with respect to both local and coupled constraints and the closed-loop stability of the whole system are guaranteed. In final, the numerical results of the comparisons between the DMPC algorithm and the centralised model predictive control(CMPC) are given to show the effectiveness of the proposed algorithm. The results show that the DMPC algorithm not only dramatically decreases the optimizing time but also maintains most of the control performance of CMPC.2. A DMPC algorithm is investigated for the consensus of second-order nonlinear multi-agent systems with coupled cost. All the agents share one reference trajectory. With the synchronous update strategy, a time-varying compatibility constraint, which plays an important to ensure the stability, is presented to ensure that the actual state trajectory of each subsystem does not deviate too much from its assumed one. Furthermore, a positively invariant terminal region and a corresponding auxiliary controller are developed for each agent. Given the designed terminal ingredients and compatibility constraints,the recursive feasibility and closed-loop stability of the whole system are guaranteed. A numerical example of 2-Degree-of-Freedom(2-DoF) robotic manipulator illustrates the efficacy of the proposed algorithm.3. A DMPC algorithm is explored for the formation of second-order linear multiagent systems with collision avoidance. With the synchronous update strategy, the improved compatibility constraints with respect to both the position compatibility and the state compatibility, are designed for each agent. The collision avoidance constraints are tightened by replacing the actual positions of each agent’s neighbors with their assumed ones. By using the second-order model and the formation, the terminal ingredients are designed. Particularly, the states in the positively invariant terminal sets satisfy the collision avoidance constraints. By implementing the proposed distributed optimization algorithm,the recursive feasibility of the optimization problem, the closed-loop stability of the whole system and the collision avoidance between agents are guaranteed. A numerical example illustrates the effectiveness of the proposed algorithm.At the end of this dissertation, the main results are concluded and the problems to be solved in the future are presented.