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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 paper, the output consensus of a class of linear heterogeneous multi-agent systems with unmatched disturbances is considered. Firstly, based on the relative output information among neighboring agents, we propose an asymptotic sliding-mode based consensus control scheme, under which, the output consensus error can converge to zero by removing the disturbances from output channels. Secondly, in order to reach the consensus goal, we design a novel high-order unknown input observer for each agent. It can estimate not only each agent’s states and disturbances, but also the disturbances’ high-order derivatives, which are required in the control scheme aforementioned above. The observer-based consensus control laws and the convergence analysis of the consensus error dynamics are given. Finally, a simulation example is provided to verify the validity of our methods. [ABSTRACT FROM AUTHOR]

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]

Integrative design of communication mechanism and coordinated control law is an interesting and important problem for multi-agent networks. In this paper, we consider distributed coordination of discrete-time second-order multi-agent systems with partially measurable state and a limited communication data rate. A quantized-observer based encoding-decoding scheme is designed, which integrates the state observation with encoding/decoding. A distributed coordinated control law is proposed for each agent which is given in terms of the states of its encoder and decoders. It is shown that for a connected network, 2-bit quantizers suffice for the exponential asymptotic synchronization of the states of the agents. The selection of controller parameters and the performance limit are discussed. It is shown that the algebraic connectivity and the spectral radius of the Laplacian matrix of the communication graph play key roles in the closed-loop performance. The spectral radius of the Laplacian matrix is related to the selection of control gains, while the algebraic connectivity is related to the spectral radius of the closed-loop state matrix. Furthermore, it is shown that as the number of agents increases, the asymptotic convergence rate can be approximated as a function of the number of agents, the number of quantization levels (communication data rate) and the ratio of the algebraic connectivity to the spectral radius of the Laplacian matrix of the communication graph. [ABSTRACT FROM AUTHOR]