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In this article, the effects of different models on the controllability of leader‐follower dynamics system based on Laplacian matrix are studied, and the controllability results applicable to general model are obtained. Our research is based on three different control modes, namely, broadcast control, UI$$ {U}_I $$ control, and non‐broadcast control, which cover all the control modes in the general model. Specifically, we first identify the relation of different UI$$ {U}_I $$ control, that is, if the system is controllable under i1$$ {i}_1 $$ different control signals, then increasing the number of control signals does not change the controllability of the system. Furthermore, it is proved that in a fixed topology, when the number of control inputs is increased, the controllability of the system is not correlated with the controllability of the original system, which appears counter‐intuitive. But the spectral radius of the Gramian matrix of the controllable system is increased. In addition, we analyze the condition number of Gramian matrix. Based on the above conclusions, we put forward the concept of hierarchical equivalent partition (HEP), and prove that under the general model, the existence of HEP makes the system uncontrollable. Finally, we expect to find a way to make the system controllable under the general model. Therefore, we obtain sufficient conditions for the system to be controllable. As a by‐product, we find that there is no completely uncontrollable graph when the general model with broadcast control is removed. [ABSTRACT FROM AUTHOR]

In this paper, the structural controllability of leader–follower systems over digraphs is discussed. Firstly, with the aid of leader–follower partition, we analyze the topological characteristics of systems without dilations. Moreover, we divide the digraph into the leader subgraph and the follower subgraph. By analyzing the topological characteristics of the follower subgraph, a sufficient condition to ensure the system structurally controllable is given. Furthermore, some special topologies of follower graphs are analyzed, such as unidirectional cycle graphs and directed paths, and the corresponding sufficient conditions of structural controllability are given. Meanwhile, a method to construct digraphs with structural controllability is presented. Finally, the strong structural controllability of directed tree graphs is considered, as well as the selection mechanism of leaders and the lower bound of the number of leaders under strong structural controllability are given. The above results reflect the effects of topologies on strong (or weak) structural controllability. [ABSTRACT FROM AUTHOR]

Based on the Jordan form of system matrix, this paper discusses algebraic conditions for the controllability of the multiagent network system with directed graph from two aspects: leader-follower network attribute and coupling input disturbance. Leader-follower network attribute refers to the topology structure and information communication among agents. Coupling input disturbance includes the number of external coupling inputs and the selection of leader nodes. When the leader-follower network attribute is fixed, the selection method of coupling input disturbance is studied for the controllability, and when the coupling input disturbance is known, we derive necessity and sufficiency conditions to determine the controllability. The reliability of theoretical results is verified by numerical examples and model simulation. Besides, the generally perfect controllability is introduced, that is, the system is always controllable regardless of the number and the locations of leaders. In practical engineering applications, the perfectly controllable topology can improve the system fault tolerance and accelerate the commercialization process, which has a profound significance for promoting the modernization process. [ABSTRACT FROM AUTHOR]

Stabilizing multiagent systems including unstable agents shows the advantage of cooperation. This paper addresses the problem of stabilization of heterogeneous multiagent systems. Under cycle graphs, a sufficient condition for the stabilization problem via harmonic control is provided and an algorithm of designing the interconnection gains is presented. Furthermore, a sufficient and necessary condition for stabilization problem via harmonic control under cycle graphs is first given when the graph contains less than 5 nodes. [ABSTRACT FROM AUTHOR]

This paper studies the controllability of multiagent systems based on path and cycle graphs. For paths or cycles, sufficient and necessary conditions are presented for determining the locations of leaders under which the controllability can be realized. Specifically, the controllability of a path is shown to be determined by a set generated only from its odd factors, and the controllability of a cycle is determined by whether the distance between 2 leaders belongs to a set generated from its even (odd) factors when the number of its nodes is even (odd). For both graphs, the dimension of the controllable subspace is also derived. Moreover, the technique used in the derivation of the above results is further used to get sufficient and necessary conditions for several different types of graphs generated from path and cycle topologies. These types of graphs can be regarded as typical topologies in the study of multiagent controllability, and accordingly the obtained results have meaningful enlightenment for the research in this field. [ABSTRACT FROM AUTHOR]

In this paper, the controllability of multi-agent systems is studied under leader-follower framework, where the interconnection between agents is directed. The concept of leader-follower connectedness is first introduced for directed graph to check controllability, and some graph-theoretic conditions are derived for constructively designed topologies. Then, distance partition and almost equitable partition are employed to quantitatively study the controllable subspaces. Moreover, the relationship between the state invariance of multi-agent systems and the existence of almost equitable partition is discussed. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper considers the controllability problem for both continuous- and discrete-time linear heterogeneous multi-agent systems with directed and weighted communication topology. First, two kinds of neighbour-based control protocols based on the distributed protocol of first-order and second-order multi-agent systems are proposed, under which it is shown that a heterogeneous multi-agent system is controllable if the underlying communication topology is controllable. Then, under special leader selection, the result shows that the controllability of a heterogeneous multi-agent system is solely decided by its communication topology graph. Furthermore, some necessary and/or sufficient conditions are derived for controllability of communication topology from algebraic and graphical perspectives. Finally, simulation examples are presented to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the controllability of first-order and second-order discrete-time multi-agent systems with directed topology and input delay. The problem is studied in the leader–follower framework where a number of agents are selected to be leaders and serve as control inputs to all other agents. Sufficient and necessary conditions are derived for the controllability of first-order discrete-time multi-agent systems. With sampling period and feedback gain satisfying certain conditions, it is proved under three different protocols that the controllability of second-order discrete-time multi-agent systems is equivalent to that of a pair of submatrices of Laplacian matrix. In addition, the controllability of both first-order and second-order discrete-time multi-agent systems with input delay is shown, through some transformations, to be equivalent to that of the transformed non-delayed systems. Finally, some simulation examples are given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: By controllability of multi-agent systems, we mean the property that all agents can be driven to arbitrary configurations only through regulating a few leaders externally, while the rest of the agents are subject to the nearest-neighbor-law. It is known that the controllability of multi-agent systems depends not only on the communication topologies among agents but also on the selection of leaders. The main objective of this paper aims to characterize the virtue that leaders should have from the perspective of algebraic and graphical conditions. We begin with a heuristic observation for tree graph. To gain more insights, necessary and sufficient conditions are then proposed in terms of downer branch and subgraphs, respectively. In particular, it is shown for path topologies that controllability completely depends on the leaders’ location. The obtained results may help us to pave the way towards a new method of formation and reconfiguration control in swarming robots. [Copyright &y& Elsevier]