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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.

We study the problem of optimal dynamic pricing for a monopolist selling a product to consumers in a social network. The only means of spread of information about the product is via Word of Mouth communication; consumers' knowledge of the product is only through friends who have already made a purchase. By analyzing the structure of the underlying endogenous process, we show that the optimal dynamic pricing policy for durable products drops the price to zero infinitely often, giving away the immediate profit in full to expand the informed network in order to exploit it in future. We provide evidence for this behavior from smartphone applications, where price histories indicate frequent free-offerings for many apps. Moreover, we show that despite infinitely often drops of the price to zero, the optimal price trajectory does not get trapped near zero. When externalities are present, we show that a strong enough network externality can push the price drops to a nonzero level, but similar price fluctuations to this new price floor still remain. When the product is nondurable, we show that the fluctuations disappear after a finite time.

In this paper, structural controllability of a leader-follower multi-agent system with multiple leaders is studied. A graphical condition for structural controllability based on the information flow graph of the system is provided. The notions of plink and q-agent controllability in a multi-leader setting are then introduced, which provide quantitative measures for the controllability of a system which is subject to failure in the agents and communication links. The problem of leader localization is introduced, which is concerned with finding the minimum number of agents whose selection as leaders results in a p-link or q-agent controllable network. Polynomial-time algorithms are subsequently presented to solve the problem for both cases of undirected and directed information flow graphs.