text: Network connectivity plays an important role in the information exchange between different agents in the multi-level networks. In this paper, we establish a game-theoretic framework to capture the uncoordinated nature of the decision-making at different layers of the multi-level networks. Specifically, we design a decentralized algorithm that aims to maximize the algebraic connectivity of the global network iteratively. In addition, we show that the designed algorithm converges to a Nash equilibrium asymptotically and yields an equilibrium network. To study the network resiliency, we introduce three adversarial attack models and characterize their worst-case impacts on the network performance. Case studies based on a two-layer mobile robotic network are used to corroborate the effectiveness and resiliency of the proposed algorithm and show the interdependency between different layers of the network during the recovery processes.
  @cite_29: 
  @cite_6: We consider the problem of maximizing the algebraic connectivity of the communication graph in a network of mobile robots by moving them into appropriate positions. We describe the Laplacian of the graph as dependent on the pairwise distance between the robots and formulate an approximate problem as a Semi-Definite Program (SDP). We propose a consistent, non-iterative distributed solution by solving local SDP's which use information only from nearby neighboring robots. Numerical simulations show the performance of the algorithm with respect to the centralized solution.
  @cite_0: We consider the set G consisting of graphs of fixed order and weighted edges. The vertex set of graphs in G will correspond to point masses and the weight for an edge between two vertices is a functional of the distance between them. We pose the problem of finding the best vertex positional configuration in the presence of an additional proximity constraint, in the sense that, the second smallest eigenvalue of the corresponding graph Laplacian is maximized. In many recent applications of algebraic graph theory in systems and control, the second smallest eigenvalue of Laplacian has emerged as a critical parameter that influences the stability and robustness properties of dynamic systems that operate over an information network. Our motivation in the present work is to "assign" this Laplacian eigenvalue when relative positions of various elements dictate the interconnection of the underlying weighted graph. In this venue, one would then be able to "synthesize" information graphs that have desirable system theoretic properties.
  @cite_23: To accomplish cooperative tasks, robotic systems are often required to communicate with each other. Thus, maintaining connectivity of the communication graph is a fundamental issue in the field of multi-robot systems. In this paper we present a completely decentralized control strategy for global connectivity maintenance of the communication graph. Considering the disk communication model, we describe a gradient-based control strategy that exploits decentralized estimation of the algebraic connectivity. Unlike previous approaches available in the literature, the proposed control algorithm solves the global connectivity problem in a decentralized manner providing theoretical guarantees, without requiring maintenance of the local connectivity between robotic systems. Moreover, results obtained with simulations and experiments on real robots are described for demonstrating the efficacy of the proposed algorithm.
  @cite_2: In this paper, we examine optimization-based methods for designing the network topology when the desired topology should have certain global variational properties, such as minimal power consumption for information exchange links, or supporting fast convergence of consensus-based distributed protocols. We first classify the optimization-based methodology for three distinct categories, namely, for construction of optimal non-geometric networks, time-invariant geometric networks, and time-varying geometric networks. We then proceed to propose optimization-based algorithms for each class of problems that aim to allocate the limited resources, e.g., communication ranges, in the most efficient way while achieving optimal performance. Examples and applications of the developed methodology are also examined.
  @cite_5: While there has been significant progress in recent years in the study of estimation and control of dynamic network graphs, limited attention has been paid to the experimental validation and verification of such algorithms on distributed teams of robots. In this work we conduct an experimental study of a non-trivial distributed connectivity control algorithm on a team of seven nonholonomic robots as well as in simulation. The implementation of the algorithm is completely decentralized and asynchronous, assuming that each robot only has access to its pose and knowledge of the total number of robots. All other necessary information is determined via message passing with neighboring robots. We show that such algorithms, requiring complex inter-agent communication and coordination, are feasible as well as highly successful in enabling a network of robots to adapt to disturbances while preserving connectivity.
  @cite_11: 
summary: In the previous works, robotic network connectivity control problem is often addressed either in a totally centralized way @cite_5 @cite_0 @cite_29 @cite_2 , or completely decentralized way @cite_6 @cite_23 @cite_11 . The centralized framework yields an optimal network but with low resiliency, since responses to failures in a global network may not be instantaneous. The network resulting from the decentralized framework is resilient; however, it is difficult to achieve the team solution with limited coordination. Our framework stands in between these two frameworks and thus leads to balanced features in terms of resiliency and optimality.