Consensus Analysis And Control In Multi-Agent Systems

A multi-agent system is always composed of many interconnected agents, in which agents represent individual elements with their own dynamics and edges represent the relationships between their dynamics. The consensus problem is one fundamental issues in the study of the distributed control of multi-agent systems, and has attracted many attentions from a variety of areas, since the research on such problem not only helps better understand the mechanisms of natural collective phenomena, but also provides useful insights to develop formation control and distributed cooperative control for the coordination between multiple mobile autonomous robots.This thesis studies the consensus problem in networks of autonomous agents, and the main contributions of the thesis are as follows:1. This thesis investigates a group consensus problem with discontinuous information transmissions among different groups of dynamic agents.In the group consensus problem, the agents reach more than one consistent state asymptotically where the communication network of these agents is considered undirected. Then a novel group consensus protocol, called hybrid protocol, is proposed to solve this problem. The convergence analysis is presented and the algebraic criterions are established. Then, a group consensus problem is further investigated for multiple networked agents with parametric uncertainties where all the agents are governed by the Euler-Lagrange system with uncertain parameters. A novel group consensus protocol and a time-varying estimator of the uncertain parameters are proposed for each agent in order to solve the couple-group consensus problem. It is shown that the group consensus is reachable even when the system contains the uncertain parameters. Moreover, the multi-group consensus and the group consensus with switching topology are also discussed as extensions.2. This thesis addresses a consensus problem for second-order agents with unknown but bounded (UBB for short) disturbance which may affect the measure of neighbors’velocities. In this study, the communication topology of the multi-agent system is supposed to be connected. In order to solve this consensus problem, a new velocity estimation called distributed lazy rule is firstly proposed, where each agent can estimate its neighbors’velocities one by one. Then, a group of sufficient conditions for this second-order consensus problem are presented by adopting graph theory and the well-known Barbalat lemma, and the bounded consensus protocol is taken into account due to actuator saturation. Moreover, a consensus problem is investigated for a group of second-order agents with an active leader. Here, the velocity of the leader cannot be measured, while the leader and all agents are governed by the same nonlinear intrinsic dynamics. To achieve consensus in the sense of both position and velocity, a neighbor-based estimator design approach and a pinning-controlled algorithm are proposed for each autonomous agent. It is found that all agents in the group follow the leader, and the velocity tracking errors of estimators converge to zero asymptotically, without assuming that the interaction topology is strongly connected or contains a directed spanning tree. When considering switching topologies between leader and followers, similar results are obtained.3. This thesis investigates the consensus problem for a group of first-order agents in the cooperation-competition network, where agents can cooperate or even compete with each other, i.e., the elements in the coupling weight matrix of the graph can be either positive or negative. In order to solve this consensus problem, the whole network is firstly divided into two sub-networks, i.e., the cooperation sub-network and the competition sub-network, and then two kinds of time-delayed control schemes are designed in the competition sub-network. By combining the Lyapunov theory together with the synchronization manifold method, several effective sufficient conditions of consensus are provided, which means that the competition relationships could help the agents achieve consensus under the time-delayed control designed in the competition sub-network. Moreover, the results are also extended to the pure competition networks where all the elements in the weight matrices are either zeros or negative. Furthermore, the consensus problem of second-order multi-agent systems with switching topologies is investigated by designing a time-delayed impulsive consensus control scheme, where all the agents are governed by the same nonlinear intrinsic dynamics and they can either cooperate or compete with each other. By establishing a comparison system, a new comparison principle method is successfully applied to study such consensus problem. Then, several effective sufficient conditions are attained without assuming that the interaction topology is strongly connected or contains a directed spanning tree.Finally, we review the results presented in this thesis, and outline research directions which spring from this thesis.