This thesis mainly studies the distributed optimization control of the multi-agent systems. The problems of the optimal distributed control, suboptimal dis-tributed control and the decentralized control for the linear quadratic multi-agent systems have been investigated and searched in great depth and a series of results have been obtained. Multi-agent systems are large-scale networked control systems which are made up of some intelligent units, such as mobile robot, air vehicle, single economy, individual organism, etc., and the communication networks between them. They exist in industry, economic, social, control science and many other fields. In multi-agent systems, there is no centralized global control strategy and the tradi-tional control method and theory could not directly applied to the networked control system, so the distributed control which use the local information have been widely searched and applied in the robots, aircraft consensus, formation, and tracking con-trol because of its stronger robustness, flexibility and extensibility. This paper is de-voted to the research of the distributed optimization control for the linear quadratic multi-agent systems, then enrich and perfect further the research results of networked control systems. The obtained results have important theoretical value and practical significance for the development of the theory of network systems.The main contributions and innovations are as:We get the direct relationship between the distributed controller and the weighted matrix through Riccati equa-tion and give the sufficient condition for the existence of the distributed optimal controller and its analytical form for the distributed optimal control; We design two classes of distributed controllers in which there are parameters to be optimized based on the topology of the system and give the recursive form of distributed suboptimal controller by using the dynamic programming method and the "averaged" optimiza-tion approach, and prove the existence and uniqueness of the distributed suboptimal controller and the asymptotic stability of the system for the distributed suboptimal control; We obtain the decentralized optimal controller and the centralized optimal controllers by using the special structure and state aggregation method, and prove the equivalence between them in theory for the decentralized control of the Mean Field LQ multi-agent systems with input delays.The main contents, results and innovations are listed as follows in the order of chapters:1. Consider the optimal distributed control problems for both continuous-time and discrete-time linear multi-agent systems. Based on the classical optimal control and the matrix decomposition, it is showed in theory that the optimal controller need the global information for the consensus cost function, i.e., the optimal feedback gain matrix corresponds to a complete undirected graph. The existence conditions of the distributed optimal controller for some special cost function are given. Then the an-alytical form of the distributed optimal controller is also obtained and the asymptotic stability of the system is discussed. At last, the existence conditions of the distributed optimal controller that are not satisfied are also discussed.2. For the LQR control problem of the general discrete-time multi-agent sys-tems, two classes of distributed controllers are designed and optimized. The dis-tributed suboptimal controllers are obtained and the existence and uniqueness are proved by the matrix decomposition and matrix inequality approach. Based on the limitation of the systemâ€™s topology structure, the distributed controllers of the single and double parameters for optimization are given. Using the Bellman dynamic pro-gramming method and the "averaged" optimization approach, the suboptimal feed-back gain matrices are presented and the distributed suboptimal controllers are ob-tained by the form of recursive iteration. The suboptimal feedback gain matrices depend on the system parameters, the weighted matrix of the cost function and the topological structure of the system and are independent of the state information of the system, and can be computed in off-line. Accordingly, the infinite-time dis-tributed control problems are also considered. Under mild conditions, the constant suboptimal feedback gain matrix and the distributed suboptimal controller are pre- sented. And then, the asymptotic stability of the system and the calculation method of the constant distributed suboptimal controller are discussed.3. For the discrete-time Mean Field LQ multi-agent systems with input delay, the decentralized optimal control are considered. Using the dynamic programming method and state aggregation approach, for the noncooperative case, the original LQ problem is changed to one optimal tracking control problem with delays, then the decentralized optimal controllers which are related to the feedback control of the their own state, the past historical input and the solutions of a iterative equation are got, which are unrelated to the states of other agents and the network topology of the system. When the multi-agent system is cooperative, a common social performance index is optimized and the centralized optimal controllers are also obtained. Then they are proved that the optimal controllers and the optimal cost function of the decentralized control and the centralized control are equivalent for the multi-agent control problem. |