Research On Group Consensus And Formation Control Of Multi-agent Systems

In recent years, with the rapid development of computer and communication technology, coordinated control of multi-agent systems has become a hot topic in control theory and its mathematical method. As one fundamental issue in coordinated control, the consensus problem has attracted increasing attention of researchers. The group consensus problem, as its emerging sub-topic, is mainly concerned with diverse consensus states asymptotically reached in multi-agent systems. Formation control, closely related with consensus problem, is an important issue in coordinated control of multi-agent systems.This dissertation studies group consensus problem in many cases, and also analyszes formation control of multi-agent systems with time-varying delays. The main results of this dissertation are as follows:1. This dissertation studies the group consensus problem of first-order multi-agent systems with a real leader and second-order multi-agent systems with virtual leaders,namely, leader-following group consensus problem. For first-order systems, we first propose a continuous-time group consensus protocol, on the basis of which we further provide a group consensus protocol with sampled-data information. By utilizing matrix theory, we obtain conditions on the interaction topology, the control parameter and the sampling period to ensure the solvability of the group consensus problem. For secondorder systems with virtual leaders, by constructing the distributed observers, we propose a group consensus protocol based only on position measurements, and the group consensus problem is proved to be solvable under undirected and connected topology.2. This dissertation studies the group consensus problem for leaderless multi-agent systems under two circumstances, namely, without and with time-delays. For the case of fixed topology without time-delays:1) For the continuous-time system with inherent nonlinear dynamics, we convert the the group consensus problem into the stability problem of the error system by linear transformation; 2) For the general continuous-time and discrete-time systems, we divide the agents under group spanning tree into zero in-degree groups and nonzero in-degree groups, and then by employing algebraic graph theory and matrix theory, we not only derive the topology conditions for the solvability of the group consensus problem, but also prove that the nonzero in-degree groups finally converge to convex combination of the consensus states of the zero in-degree groups. For the case of switching topology with time-delays, the continuous-time time-delays system is equivalently transformed into its augmented system. By analyzing the convergence of the augmented system, we prove that with bounded time-delays, the system can solve the group consensus problem, if the union of the interaction topology across any time interval with a given length contains a group spanning tree.3. The leader-following consensus problem with time-varying delays is addressed.For second-order multi-agent systems with a leader, the communication time-delays might exist in the transmission of both velocity and position, and the velocity of the leader is not necessarily a constant. By applying Lyapunov stability theory, we obtain the topology conditions under fixed topology and switching topology respectively, for the solvability of the consensus problem. Additionally, a kind of formation control problem with time-varying delays is converted into the consensus problem, and finally, the topology conditions and the upper bounds of the allowable time-delays, are obtained for the attainment of both time-invariant and time-varying formations as well as for time-varying formations for trajectory tracking.4. The consensus problem for multi-agent systems with multiple time-varying delays is investigated. By introducing coordinate transformation, we transform the systems under fixed and switching topologies into their respective reduced-order systems. Then,by analyzing the asymptotic stability of the reduced-order systems, we obtain the topology conditions and the upper bounds of the allowable time-delays, for the solvability of the consensus problem. Besides, we take into account the formation control problem of second-order systems with multiple time-varying delays, and derive the topology conditions which guarantee the attainment of the expected formations.