Consensus Problems For Multi-Agent Systems

With the progress of society and the rapid development of science and technology, the modeling and coordination control problem of multi-agent systems have become a hot spot in many research fields, because it can be widely utilized in these fields. Consensus problem is one of the most fundamental problems of coordinated control. The basic idea to solve consensus problem is to design suitable protocols or algorithms making the system reach global consensus. Based on the existing research results, this paper studies the consensus problems of the multi-agent systems much more thoroughly and systematically by using the control theory, stability theory, algebra graph theory. The main contents of this dissertation are given in the following.1.The leader-following consensus problem of high order multi-agent systems with time-varying communication delays and noises is considered. The dynamics of each agent and the leader is a linear system. In order to weaken the influence of noise, a time-varying neighbor-based control of each following agent is designed in using local information. The control design technique is based on algebraic graph theory, Riccati inequality and Lya-punov inequality. By using Lyapunov-Razumikhim and stochastic analysis methods, we prove that the closed loop tracking control system is stochastically stable in mean square and the estimation errors converge to zero in mean square as well.2. The leader-following consensus problem of discrete-time multi-agent systems is considered. The dynamics of the leader and all following agents adopt the same general form of a linear model that can be any order. The interconnection topology among the agents is assumed to be switching and undirected. To track the active leader, two kinds of distributed observer-based consensus protocols are proposed for each following agent, whose distributed observers are used to estimate leader's state and tracking error based on the relative outputs of neighboring agents, respectively. In light of the modified discrete- time algebraic Riccati equality and Lyapunov method, we prove that the discrete-time leader-following consensus problem can be solved by proposing the distributed observer-based consensus protocol under switching topologies.3.We focus on the consensus problem for leaderless and leader-followers multi-agent systems with periodically intermittent control. The dynamics of each agent in the system is a linear system, and the interconnection topology among the agents is assumed to be switching. We assume that each agent can only share the outputs with its neighbors. There-fore, a class of distributed intermittent observer-based consensus protocols are proposed for each agent. The control parameters used in protocol can be constructed by solving the Riccati equation and the Sylvester equation. The parameter-dependent common Lyapunov function method is involved to analyze the consensus problems under undirected switching topology. And our results show that the consensus criteria depends on the ratio of control width to control period.4. Motivated by the concept of finite-time stability, the concept of finite-time con-sensus is proposed, and the finite-time consensus problem of leader-following multi-agent systems is investigates. Two distributed consensus protocols based on its state and its out-put, respectively, are proposed to solve finite -time consensus. In light of linear matrix inequalities, some sufficient conditions are established to ensure that the multi-agent sys-tem achieves finite-time consensus. Furthermore, we discuss the discrete-time counterpart along the similar lines.5.Motivated by the situation where agents can only take the output feedback for the distributed control design and the input of the leader is unknown to each follower, a novel class of protocols have been designed in this paper to solve the distributed consensus track-ing problem. However, the agents can not achieve consensus if the coupling c is not big enough. To compensate this shortcoming, a distributed adaptive consensus tracking proto-col is designed to solve the consensus tracking problems in fully distributed fashion, which also can avoid high gain control.