Distributed Model Predictive Consensus via the Alternating Direction Method of Multipliers

We propose a distributed optimization method for solving a distributed model predictive consensus problem. The goal is to design a distributed controller for a network of dynamical systems to optimize a coupled objective function while respecting state and input constraints. The distributed optimization method is an augmented Lagrangian method called the Alternating Direction Method of Multipliers (ADMM), which was introduced in the 1970s but has seen a recent resurgence in the context of dramatic increases in computing power and the development of widely available distributed computing platforms. The method is applied to position and velocity consensus in a network of double integrators. We find that a few tens of ADMM iterations yield closed-loop performance near what is achieved by solving the optimization problem centrally. Furthermore, the use of recent code generation techniques for solving local subproblems yields fast overall computation times.Comment: 7 pages, 5 figures, 50th Allerton Conference on Communication, Control, and Computing, Monticello, IL, USA, 201

Active influence in dynamical models of structural balance in social networks

We consider a nonlinear dynamical system on a signed graph, which can be interpreted as a mathematical model of social networks in which the links can have both positive and negative connotations. In accordance with a concept from social psychology called structural balance, the negative links play a key role in both the structure and dynamics of the network. Recent research has shown that in a nonlinear dynamical system modeling the time evolution of "friendliness levels" in the network, two opposing factions emerge from almost any initial condition. Here we study active external influence in this dynamical model and show that any agent in the network can achieve any desired structurally balanced state from any initial condition by perturbing its own local friendliness levels. Based on this result, we also introduce a new network centrality measure for signed networks. The results are illustrated in an international relations network using United Nations voting record data from 1946 to 2008 to estimate friendliness levels amongst various countries.Comment: 7 pages, 3 figures, to appear in Europhysics Letters (http://www.epletters.net

Bounding bias due to selection

When epidemiologic studies are conducted in a subset of the population, selection bias can threaten the validity of causal inference. This bias can occur whether or not that selected population is the target population, and can occur even in the absence of exposure-outcome confounding. However, it is often difficult to quantify the extent of selection bias, and sensitivity analysis can be challenging to undertake and to understand. In this article we demonstrate that the magnitude of the bias due to selection can be bounded by simple expressions defined by parameters characterizing the relationships between unmeasured factor(s) responsible for the bias and the measured variables. No functional form assumptions are necessary about those unmeasured factors. Using knowledge about the selection mechanism, researchers can account for the possible extent of selection bias by specifying the size of the parameters in the bounds. We also show that the bounds, which differ depending on the target population, result in summary measures that can be used to calculate the minimum magnitude of the parameters required to shift a risk ratio to the null. The summary measure can be used to determine the overall strength of selection that would be necessary to explain away a result. We then show that the bounds and summary measures can be simplified in certain contexts or with certain assumptions. Using examples with varying selection mechanisms, we also demonstrate how researchers can implement these simple sensitivity analyses

Reactive point processes: A new approach to predicting power failures in underground electrical systems

Reactive point processes (RPPs) are a new statistical model designed for predicting discrete events in time based on past history. RPPs were developed to handle an important problem within the domain of electrical grid reliability: short-term prediction of electrical grid failures ("manhole events"), including outages, fires, explosions and smoking manholes, which can cause threats to public safety and reliability of electrical service in cities. RPPs incorporate self-exciting, self-regulating and saturating components. The self-excitement occurs as a result of a past event, which causes a temporary rise in vulner ability to future events. The self-regulation occurs as a result of an external inspection which temporarily lowers vulnerability to future events. RPPs can saturate when too many events or inspections occur close together, which ensures that the probability of an event stays within a realistic range. Two of the operational challenges for power companies are (i) making continuous-time failure predictions, and (ii) cost/benefit analysis for decision making and proactive maintenance. RPPs are naturally suited for handling both of these challenges. We use the model to predict power-grid failures in Manhattan over a short-term horizon, and to provide a cost/benefit analysis of different proactive maintenance programs.Comment: Published at http://dx.doi.org/10.1214/14-AOAS789 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

The effect of injector design on thrust- chamber erosion

Relation between injector design and erosion of ablative and pyrolytic graphite thrust chamber throa