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This article discusses cooperative stabilization control of rigid formations via an event-based approach. We first design a centralized event-based formation control system, in which a central event controller determines the next triggering time and broadcasts the event signal to all the agents for control input update. We then build on this approach to propose a distributed event control strategy, in which each agent can use its local event trigger and local information to update the control input at its own event time. For both cases, the triggering condition, event function, and triggering behavior are discussed in detail, and the exponential convergence of the event-based formation system is guaranteed. [ABSTRACT FROM AUTHOR]

This work focuses on the construction of rigid formation from non‐rigid ones in the two‐dimensional space. Analogously to operations of Henneberg sequence aiming to guarantee the minimal rigidity of formation, two new operations are introduced, allowing one to sequentially build any rigid graph by connecting non‐rigid ones. A systematic construction sequence is developed based on proposed operations, and is shown to be able to restore rigidity by introducing minimum number of new edges during the construction process. Further applications of the proposed operations are also presented, one of which is successfully employed in the problem of persistence analysis of directed graphs, and can verify the persistence of a given graph with a speed two times faster comparing with existing solution. [ABSTRACT FROM AUTHOR]

This paper considers mainly the leader-following consensus for multiple agents with general linear system dynamics under switching topologies. Three different settings are systematically considered. We first consider the setting that the underlying interaction topologies switch arbitrarily among the possible weakly connected digraphs and then extend it to a more general setting that the weak connectivity of the interaction topologies is kept for some disconnected time intervals with short length due to the communication constraints among agents. Exponentially, consensus control is proved to be achieved, and the convergence rate can be specified as well for both settings in spite of the relaxed conditions on the system dynamics of each individual agent which even allow that each agent has exponentially unstable mode, while for the last case where the weak connectivity is only maintained on the joint of the interaction topologies, consensus control is proved to be achieved when the system matrix of each individual agent satisfies certain stability conditions. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the asynchronous consensus problem of discrete-time second-order multi-agent system under dynamically changing communication topology, in which the asynchrony means that each agent detects the neighbors' state information to update its state information by its own clock. It is not assumed that the agents' clocks are synchronized. Nor is it assumed that the time sequence over which each agent update its state information is evenly spaced. By using tools from graph theory and nonnegative matrix theory, particularly the product properties of row-stochastic matrices from an infinite set, we finally show that essentially the same result as that for the synchronous discrete-time system holds in the face of asynchronous setting. This generalizes the existing result to a very general case. [ABSTRACT FROM PUBLISHER]

This brief presents a new distributed scheme to solve the consensus problem for a group of agents if neither their absolute states nor inter-agent relative states are available. The new scheme considers a random partition of agents into two subgroups at each step and then uses the relative group representative state as feedback information for the consensus purpose. It is then shown that almost sure consensus can be achieved under the proposed scheme in both discrete time and continuous time. For the discrete time case, almost sure consensus is achieved if and only if the weighting parameter for state update is greater than one. For the continuous time case, almost sure consensus is realized when the weighting parameter is positive. Moreover, it is shown that if a uniform probability is considered for group selection, then the group of agents can reach average consensus in mean. [ABSTRACT FROM AUTHOR]

Abstract: The paper introduces complex-valued Laplacians for graphs whose edges are attributed with complex weights and studies the leader–follower formation problem based on complex Laplacians. The main goal is to control the shape of a planar formation of point agents in the plane using simple and linear interaction rules related to complex Laplacians. We present a characterization of complex Laplacians that preserve a specific planar formation as an equilibrium solution for both single integrator kinematics and double integrator dynamics. Planar formations under study are subject to translation, rotation, and scaling in the plane, but can be determined by two co-leaders in leader–follower networks. Furthermore, when a complex Laplacian does not result in an asymptotically stable behavior of the multi-agent system, we show that a stabilizing matrix, which updates the complex weights, exists to asymptotically stabilize the system while preserving the equilibrium formation. Also, algorithms are provided to find stabilizing matrices. Finally, simulations are presented to illustrate our results. [Copyright &y& Elsevier]