Research On Consensus Problems And Containment Control Problems Of Multiagent Systems

Due to the wide applications in military and civilian areas, distributed coordinationcontrol of multiagent systems has received compelling attention from various researchcommunities, and it has been an active area of research. Consensus is an important andessential problem in coordination control of multiagent systems. In this thesis, consen-sus problems of multiagent systems with sampled-data information, switching topology,communication delay and measurement noises are intensively investigated. Additionally,containment control of multiagent systems with multiple leaders is also studied, which isalso an important research topic in coordination control of multiagent systems. The maincontributions of this thesis can be summarized as follows:1. This thesis studies the leader-following consensus for second-order multiagentsystems. In many applications, the information exchange among the group of agents mayonly occur at discrete sampling instants. The leader-following consensus with sampled-data information is firstly investigated. On the basis of the former work, a distributed pro-tocol with sampled-data information is proposed to track an active leader-agent, and theproposed protocol utilizes only the position of neighbors’. By employing matrix theory,the conditions on the sampling period and the control parameters are derived to ensure thatthe tracking errors are ultimately bounded. Secondly, the leader-following consensus withdirected switching topologies is studied. The algebraic properties of a kind of digraphsare derived by means of the properties of M-matrices, and based on these properties thecondition on the network topology to ensure consensus is derived, and the condition onthe network topology is further weakened.2. This thesis studies the consensus problem of second-order multiagent systemswith multiple time-varying delays. In the study of consensus problems, time-delay isone of the key factors that influence the system stability. During the analysis, the con-sensus problem is simplified into the stability problem of the reduced-order system byperforming a system transformation. In the existing works concerning the same prob-lem, the condition on the time-delay is presented in terms of linear matrix equalities.In this thesis, an implicit formula for the allowable time-delay is derived by employingLyapunov-Razumikhin function. 3. This thesis studies the consensus problem of multiagent systems with measure-ment noises. In real applications, the information exchange between agents may be cor-rupted by noises, which results in the fact that each agent can only receive noisy measure-ments of its neighbors’. The case of having sampled-data information is firstly studied,and by using stochastic stability theory and algebraic graph theory, conditions on the net-work topology are presented to ensure that the system solves strong consensus problemsfor both fixed topology and switching topology. The consensus problem for continuous-time multiagent system with measurement noises is also studied. By employing stochasticstability theory and algebraic graph theory, the condition on the network topology is pre-sented to ensure that the system solves the mean square consensus for both fixed topologyand switching topology.4. This thesis studies the containment control problem of multiagent systems. Firstly,we investigate the discrete-time and continuous-time model under switching topologiesin the absence of noisy measurements. Based on nonnegative matrix theory and algebraicgraph theory, we provide the weakest condition on the network topology to ensure that thesystem solves the containment control problem. In the presence of measurement noises,a distributed protocol is proposed to solve the containment control problem. It is showedthat the system solves the strong and mean square containment control problem as longas the network topology contains a united spanning tree.