Finite-Time Consensus Problem For Multi-Agent Systems With Time-Delays

In recent years, with the wide application of distributed networks and multi-agent systems, the cooperative control problem has been brought into focus. As the basis of coordination problem for multi-agent systems, the consensus problem has played a key role in the field of control science. In multi-agent system, finite-time consensus refers to some of the agents’states achieve the same value with infinite time; finite-time consensus algorithm is a protocol for making agents reach finite-time consensus according to local information from its neighbors.The main contents and achievements of this dissertation are summarized as follows:We investigate the finite-time stabilization problem for a class of nonholonomic chained form systems with perturbed terms. With the method of Lyapunov and time-rescaling technique which is used to coordinate the convergence velocity of two subsystems, we construct control schemes in accordance with various initial states for making the nonholonomic chained form systems with perturbed terms converge to equilibrium state in any given settling time. Then the effectiveness of proposed control method is verified via numerical simulations.We then study the finite-time consensus problem of multiple nonholonomic mobile agents. Based on Lyapunov method, the control algorithm is proposed and its theoretical proof is given. Then the effectiveness of proposed control method is verified via numerical simulations.Finally, we consider the finite-time agreement problem of multi-agent systems with communication delays. We study two cases of communication topology, case1: time-invariant unidirectional; case 2: time-invariant and contains a spanning tree, each strongly connected component of the topology is detail-balanced. Based on Lyapunov method, the control algorithm is proposed and its theoretical proof is given. At last, the effectiveness of proposed control method is verified via numerical simulations.