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In this paper, structural controllability of a leader-follower multi-agent system with multiple leaders is studied from a graph-theoretic point of view. The problem of preservation of structural controllability under simultaneous failures in both the communication links and the agents is investigated. The effects of the loss of agents and communication links on the controllability of an information flow graph are previously studied. In this work, the corresponding results are exploited to introduce some useful indices and importance measures that help characterize and quantify the role of individual links and agents in the controllability of the overall network. Existing results are then extended by considering the effects of losses in both links and agents at the same time. To this end, the concepts of joint (r, s)−controllability and joint t−controllability are introduced as quantitative measures of reliability for a multi-agent system, and their important properties are investigated. Lastly, the class of jointly critical digraphs are introduced and it is stated that if a digraph is jointly critical, then joint t−controllability is a necessary and sufficient condition for remaining controllable following the failure of any set of links and agents, with cardinality less than t. Various examples are exploited throughout the paper to elaborate on the analytical findings.

This paper considers the structural controllability of a leader-follower multi-agent system. Graphical conditions for structural controllability based on the information flow graph of the system are provided. Then, the notions of plink and q-agent controllability are introduced as quantitative measures for the controllability of the system subject to failure in communication links or agents. Necessary and sufficient conditions for the system to remain structurally controllable in the case of the failure of some of the communication links or loss of some agents are derived in terms of the topology of the information flow graph. Moreover, a polynomial-time algorithm for determining the maximum number of failed communication links under which the system remains structurally controllable is presented (which can be analogously developed for the case of agents loss). Finally, the proposed algorithm is extended to the case of loss of agents.

This paper is concerned with the connectivity preservation of a group of unicycles using a novel distributed control scheme. The proposed local controllers are bounded, and are capable of maintaining the connectivity of those pairs of agents which are initially within the connectivity range. Each local controller is designed in such a way that when an agent is about to lose connectivity with a neighbor, the lowest-order derivative of the agent's position that is neither zero nor perpendicular to the edge connecting the agent to the corresponding neighbor, makes an acute angle with this edge, which is shown to result in shrinking the edge. The proposed methodology is then used to develop bounded connectivity preserving control strategies for the consensus problem as one of the unprecedented contributions of this work. The theoretical results are validated by simulation.