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Inspired by the interesting findings regarding the hierarchy and coordination of pigeons in Nagy et al.  [Nature, 2010], we revisit the discrete-time leader–follower consensus problem with switching topologies. The purpose of this paper is to investigate the impact of hierarchical topologies and followers’ self-loops on the convergence performance of leader–follower consensus, including the convergence rate and robustness to switching topologies. We first study the fixed topology case, and show that the followers converge to the leader's state in finite time if and only if each follower has no self-loops and the topology is hierarchical. However, we show via counterexample, that leader–follower consensus may not be achieved when some followers have no self-loops and the topology is switching; even if each interaction graph has a spanning tree rooted at the leader. With the aid of binary relation theory, we further develop a new approach to present a novel sufficient condition for leader–follower consensus with switching topologies and with some followers having no self-loops. We prove that when no followers have self-loops and the same hierarchical organization is kept under the switching topologies, then the fastest rate of convergence in leader–follower consensus can be achieved; even in the presence of complex dynamic topologies. This is consistent with the natural phenomena found in pigeons by Nagy et al. [ABSTRACT FROM AUTHOR]

In this note, a switching-type delay-adaptive predictor feedback controller is proposed to globally stabilize linear systems with unknown input delay. The idea of our method is to take advantage of the robustness of feedback laws to delay estimate error that is sufficiently small. We first prove that, when the delay estimate is sufficiently close to the true delay, there is a Lyapunov–Krasovskii functional that is strictly decreasing, and asymptotic regulation is achievable. Then, with the help of the Lyapunov–Krasovskii functional as a supervisor, the switching logic plays the role of adjusting the estimated delay online to make it sufficiently close to the true delay. The result of this note shows that, global adaptive stabilization of linear systems with unknown input delay is achievable, with a logic-based switching control law. [ABSTRACT FROM PUBLISHER]

A fault-tolerant observer design methodology is proposed. The aim is to guarantee a minimum level of closed-loop performance under all possible sensor fault combinations while optimizing performance under the nominal, fault-free condition. A novel approach is proposed to tackle the combinatorial nature of the problem, which is computationally intractable even for a moderate number of sensors, by recasting the problem as a robust performance problem, where the uncertainty set is composed of all combinations of a set of binary variables. A procedure based on an elimination lemma and an extension of a semidefinite relaxation procedure for binary variables is then used to derive sufficient conditions (necessary and sufficient in the case of one binary variable) for the solution of the problem which significantly reduces the number of matrix inequalities needed to solve the problem. The procedure is illustrated by considering a fault-tolerant observer switching scheme in which the observer outputs track the actual sensor fault condition. A numerical example from an electric power application is presented to illustrate the effectiveness of the design. [ABSTRACT FROM PUBLISHER]

In this technical note a decentralized controller-observer scheme for a multi-agent system is presented. The key idea is to develop, for each agent, an observer of the collective system's state and a motion controller. The observer is updated using only information from the agent itself and from its neighbors; the motion controller is designed in order to allow the team's weighted centroid to track an assigned time-varying reference. Convergence of the overall scheme is proven for directed and undirected communication graphs; moreover the extensions to the case of switching communication topologies and to the presence of saturation in the control input are discussed. Finally, numerical simulations are illustrated to validate the approach. [ABSTRACT FROM AUTHOR]

In this paper, we present a new sensor fault tolerant control scheme for linear, discrete-time systems. The scheme consists of a bank of estimators, each associated with a sensor or group of sensors, a mechanism for the detection and identification of sensor transitions from healthy-to-faulty and faulty-to-healthy operation, an estimate reconfiguration module, and an estimate-based feedback controller with reference tracking. The detection and identification approach is based on the separation of “healthy” and “faulty” sets, where appropriately selected residual variables remain under healthy or faulty operation, from “after-fault” and “after-recovery” sets, towards which the residual variables “jump” when abrupt sensor faults or recoveries occur in one or more groups of sensors. This “set-separation” approach provides pre-checkable fault tolerance guarantees whenever certain conditions, given in terms of system's known data such as plant and estimator dynamics and bounds on reference and disturbance signals, are satisfied. [ABSTRACT FROM PUBLISHER]