Analysis And Design Of Control Protocols For Low-Order Multi-Agent Systems

Multi-agent systems are a class of important and extensively existing dynamic systems, which describe that multiple agents accomplish a complex task together by sharing information, cooperating and task assignment. Therefore, multi-agent systems arouse the considerable attention among researchers. As the industrial needs and the development of science, in the last three decades, multi-agent systems have been devel-oped greatly. A large number of theoretical results have been obtained in the consensus problem, the flocking problem, the cluster synchronization problem, and some of them have been implied to the formation of unmanned aircraft, the data fusion of complex network and the coordination cooperation of multiple robots.This paper will research the design and analysis of the control protocols on the consensus problem, the flocking problem and the cluster synchronization problem. The main contents of this paper are composed of the following five parts:The first part introduces some preliminaries on algebraic graphs and Hamiltonian systems which are important for the study of multi-agent systems. Furthermore, some notations used in this paper are presented in this part.The second part studies the consensus of first-order multi-agent systems under the directed graph topology, and provides a kind of more general control protocols for the fixed and switching topologies, respectively. First, by decomposition of the state space, a necessary and sufficient condition is obtained for the consensusability of the multi-agent systems with a fixed information topology under the general control protocol. Second, utilizing the obtained necessary and sufficient condition, a new algorithm is provided to find the final consensus state based on the given initial condition. Third, for the case of switching topology, a sufficient condition is proposed for the consensusabil-ity of multi-agent systems under the general control protocol, and it is shown that the state consensus can be realized under the given conditions. Finally, several examples are studied with our presented method. Illustrative examples with simulations show that our method as well as control protocols work very well for the consensus problem of this class of linear multi-agent systems.The third part considers the consensus of second-order multi-agent systems with a directed information topology (not necessarily a balanced graph), and presents a num- ber of new results based on the following two cases:directed fixed topology and di-rected switching topology. Firstly, by the state-space decomposition, the multi-agent system is decomposed into two independent subsystems, and it is proved that the con-sensusability of the system is equivalent to the asymptotic stability of the second sub-system. Secondly, based on the equivalent relationship, two necessary and sufficient conditions are presented for the state consensus in the case of fixed information topol-ogy, and a useful method is established to determine the parameters of the designed control protocol. Thirdly, for the case of switching information topology, a sufficient condition is obtained for the consensusability of the multi-agent system under the con-dition that each graph is strongly connected and balanced. Finally, three examples are studied with our presented method. The study of illustrative examples with simulations shows that our results as well as designed control protocols work very well in studying the state consensus of this class of linear multi-agent systems.The fourth part investigates the flocking problem under the Hamiltonian frame-work. Firstly, a Hamiltonian structure is provided for the systems by choosing a kind of suitable Hamiltonian functions. Secondly, based on the provided Hamiltonian structure, two kinds of flocking control protocols are designed only by using local information of each agent. One protocol is with linear alignment rule and the other is with a kind of nonlinear alignment rule. It is shown that, following the two flocking control protocols, all the agents'velocities can converge to the same value, and stable flocking behaviors can be guaranteed. Finally, result of simulation reveals that the flocking protocols pro-posed in this paper work very well in the flocking control of multi-agent systems of "boids" model.The fifth part investigates the cluster synchronization under the undirected and di-rected topology. For the undirected topology, firstly, based on the pre-given protocol and the properties of the bipartite graph, the cluster synchronization problem is studied for the systems without time delay, and the final convergence states are given with re-spect to the initial conditions; then, the cluster synchronization problem of the systems with time delay is investigated, and the maximum allowed delay is obtained. For the directed topology, a number of new results by using the neighbor's rules are presented for the following two cases:Ⅰ) there is competition among the agents of different clus-ters, and Ⅱ) there are both competition and cooperation among the agents. Firstly, for the case Ⅰ), a linear control protocol is designed for the cluster synchronization of the multi-agent system, and a method is presented to determine the final state with the ini- tial conditions based on state-space decomposition. Secondly, we study the case II), and design a kind of control protocol based on the information of neighbors and that of two-hop neighbors (that is, neighbors'neighbors). It is shown that such a protocol can make the multi-agent system achieve the cluster synchronization faster. Finally, several examples are studied by using our presented results. The study of illustrative examples with simulations shows that our results as well as designed control protocols work very well in studying cluster synchronization of this class of multi-agent systems.Innovations of the thesis mainly include the following third aspects:●It is first that a method of state-space decomposition is presented, and is ap-plied to the study of the consensus problem of multi-agent systems. A necessary and sufficient condition is obtained under the fixed topology, and the final states are deter-mined according to the initial conditions. Furthermore, this method can deal with the consensus problem of some special directed topology under switching situation.●It is first that the flocking problem is investigated based on the Hamilton frame-work. Based on the nice structure and dissipative properties of Hamiltonian descriptor systems, two kinds of control protocol are designed and it is proved that the stable flocking behaviors can be guaranteed.●It is first that the cluster synchronization is investigated based on the competi-tive relation. Two kinds of control protocols are designed and it is proved that these protocols are effective.