In this paper, we study the finite-time consensus problems with globally bounded convergence time also known as fixed-time consensus problems for multi-agent systems subject to directed communication graphs. Two new distributed control strategies are proposed such that leaderless and leader-follower consensus are achieved with convergence time independent on the initial conditions of the agents. Fixed-time formation generation and formation tracking problems are also solved as the generalizations. Simulation examples are provided to demonstrate the performance of the new controllers.

In this paper, we investigate the fault-tolerant consensus problems for multi-agent systems with actuator faults. Based on the relative state information, fully distributed adaptive protocols are designed for these agents described by Lipschitz nonlinear dynamics under leaderless and leader-follower communication structures. As the special case, for linear multi-agent systems, fault-tolerant consensus problems are also solved with the proposed protocols. First, for the leaderless multi-agent systems, all agents reach an agreement on a common value with undirected connected communication graphs. Second, for the leader-follower multi-agent systems, in which the state of the leader is only available to a subset of the followers, the state of each follower converges to the state of the leader, asymptotically. A distinctive feature of this paper is that the adaptive protocols here are independent of the eigenvalues of the Laplacian matrix associated with the whole communication graph, which means the protocols can be implemented by each agent in a fully distributed fashion. Simulation examples are provided to illustrate the theoretical results.

In this paper, a distributed observer is designed for the state reconstruction of continuous-time linear dynamical systems with unknown inputs. Specifically, a group of sensor nodes are employed to measure the output of such a system. Due to its limited measurement, a single node may fail to reconstruct the full state. By acting on a consensus cooperative strategy, however, each node can produce an accurate state estimate, regardless of the specific input signal. The attractive performance of distributed unknown input observer relies on nothing but common neighboring communication, as well as an adequate local measurement that overlaps the effect of the unknow input along system dynamics. Correspondingly, the required network connectivity and rank conditions are given, with their linkages to the classic result being discussed.

This paper investigates a fault-tolerant leaderless consensus problem for general linear multi-agent systems (MASs) under a strongly connected directed communication graph. The influences of the actuator bias faults and loss of actuator effectiveness faults on MASs are considered in this paper. The designed fully distributed adaptive fault-tolerant consensus protocols (FTCPs) can make all agents' states achieve consensus, asymptotically. Using the features of the loss of actuator effectiveness faults and the strongly connected graph, novel positive definite Lyapunov functions are constructed skillfully to analyse the validity of the proposed protocols. Finally, simulation examples are presented to demonstrate the effectiveness of the proposed protocols.