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

Aggregation of a class of large-scale, interconnected, nonlinear dynamical systems

In this paper, the authors consider the issue of the construction of a meaningful average for a collection of nonlinear dynamical systems. Such a collection of dynamical systems may or may not have well defined ensemble averages as the existence of ensemble averages is predicated on the specification of appropriate initial conditions. A meaningful “average” dynamical system can represent the macroscopic behavior of the collection of systems and allow us to infer the behavior of such systems on an average. They can also prove to be very attractive from a computational perspective. An advantage to the construction of the meaningful average is that it involves integrating a nonlinear differential equation, of the same order as that of any member in the collection. An average dynamical system can be used in the analysis and design of hierarchical systems, and will allow one to capture approximately the response of any member of the collection

UAV Routing for Enhancing the Performance of a Classifier-in-the-loop

Some human-machine systems are designed so that machines (robots) gather and deliver data to remotely located operators (humans) through an interface in order to aid them in classification. The performance of a human as a (binary) classifier-in-the-loop is characterized by probabilities of correctly classifying objects of type $T$ and $F$. These two probabilities depend on the dwell time, $d$, spent collecting information at a point of interest (POI or interchangeably, target). The information gain associated with collecting information at a target is then a function of dwell time $d$ and discounted by the revisit time, $R$, i.e., the duration between consecutive revisits to the same target. The objective of the problem of routing for classification is to optimally route the vehicles and determine the optimal dwell time at each target so as to maximize the total discounted information gain while visiting every target at least once. In this paper, we make a simplifying assumption that the information gain is discounted exponentially by the revisit time; this assumption enables one to decouple the problem of routing with the problem of determining optimal dwell time at each target for a single vehicle problem. For the multi-vehicle problem, we provide a fast heuristic to obtain the allocation of targets to each vehicle and the corresponding dwell time