Resilient and Decentralized Control of Multi-level Cooperative Mobile Networks to Maintain Connectivity under Adversarial Environment

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.Comment: 9 pages, 6 figure

Optimal Robust Network Design: Formulations and Algorithms for Maximizing Algebraic Connectivity

This paper focuses on the design of edge-weighted networks, whose robustness is characterized by maximizing algebraic connectivity, or the smallest non-zero eigenvalue of the Laplacian matrix. This problem is motivated by the application of cooperative localization for accurately estimating positions of autonomous vehicles by choosing a set of relative position measurements and establishing associated communication links. We also examine an associated problem where every robot is limited by payload, budget, and communication to pick no more than a specified number of relative position measurements. The basic underlying formulation for these problems is nonlinear and is known to be NP-hard. We solve this network design problem by formulating it as a mixed-integer semi-definite program (MISDP) and reformulating it into a mixed-integer linear program to obtain optimal solutions using cutting plane algorithms. We propose a novel upper-bounding algorithm based on the hierarchy of principal minor characterization of positive semi-definite matrices. We further discuss a degree-constrained lower bounding formulation, inspired by robust network structures. In addition, we propose a maximum-cost heuristic with low computational complexity to find high-quality feasible solutions. We show extensive computational results corroborating our proposed methods

Output Impedance Diffusion into Lossy Power Lines

Output impedances are inherent elements of power sources in the electrical grids. In this paper, we give an answer to the following question: What is the effect of output impedances on the inductivity of the power network? To address this question, we propose a measure to evaluate the inductivity of a power grid, and we compute this measure for various types of output impedances. Following this computation, it turns out that network inductivity highly depends on the algebraic connectivity of the network. By exploiting the derived expressions of the proposed measure, one can tune the output impedances in order to enforce a desired level of inductivity on the power system. Furthermore, the results show that the more "connected" the network is, the more the output impedances diffuse into the network. Finally, using Kron reduction, we provide examples that demonstrate the utility and validity of the method