The Controllability Of Multi-agent System And Its Application

Recently, the research of multi-agent systems is an active area for researchers from various fields, such as computer science, intelligent control, network communication, social sciences and so on. The controllability of multi-agent systems is a new and significant branch. This paper studies the controllability of a series of discrete-time multi-agent systems based on existing research results, using modern control theory, matrix theory, algebra, graph theory and other theories and methods. The main contents and contributions of this paper are stated as follows:1. The controllability of discrete-time multi-agent systems with leaders on fixed topology is discussed. The quantity of the leaders is extended from one to multiple compared with the existing literatures. During the research, the vector described the information from the leaders to the followers is extended to a matrix. The main result of the controllability of the systems is derived according to the matrix theory and classical control theory. Furthermore, the model is developed to high dimensions, and the corresponding theoretic results are given on the basis of Kronecker product. These results are more general compared with the traditional researches which limit the model to one-dimension for simplicity.2. The controllability of discrete-time multi-agent systems with leaders on switching topology is presented. It is very substantial in the research of multi-agent on fixed topology. However, the topology among the agents is used to vary in the real world. The studies on varied topology are of great importance. The researchers Bo Liu etal. put forward switching topology in order to discuss the varied topology. The system is divided into some sub-systems based on switching sequence. The main results of controllability are given and the relations between the whole system and its sub-systems are investigated.3. The effect of communication time-delays in the systems on fixed topology and switching topology is considered. The case of a single time-delay and the situation of multiple time-delays are proposed, respectively. A system without time-delays on higher dimensions is introduced based on an identical transformation. The main results of controllability of the systems can be derived in the light of Rank Test in control theory. The method of PBH Test of discrete-time systems is brought forward on account of controllability decomposition, which is more concise and effective to study the controllability of discrete-time multi-agent systems.