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

Prison-Based Education and Re-Entry into the Mainstream Labor Market

We estimate the post-release economic effects of participation in prison-based General Educational Development (GED) programs using a panel of earnings records and a rich set of individual information from administrative data in the state of Florida. Fixed effects estimates of the impact of participating in the GED education program show post-release quarterly earnings gains of about 15 percent for program participants relative to observationally similar non-participants. We also show, however, that these earnings gains accrue only to racial/ethnic minority offenders and any GED-related earnings gains for this group seem to fade in the third year after release from prison. Estimates comparing offenders who obtained a GED to those who participated in GED-related prison education programs but left prison without a GED show no systematic evidence of an independent impact of the credential itself on post-release quarterly earnings.

Prison-Based Education and Re-Entry into the Mainstream Labor Market

incarceration, GED, earnings

Submodularity of Energy Related Controllability Metrics

The quantification of controllability and observability has recently received new interest in the context of large, complex networks of dynamical systems. A fundamental but computationally difficult problem is the placement or selection of actuators and sensors that optimize real-valued controllability and observability metrics of the network. We show that several classes of energy related metrics associated with the controllability Gramian in linear dynamical systems have a strong structural property, called submodularity. This property allows for an approximation guarantee by using a simple greedy heuristic for their maximization. The results are illustrated for randomly generated systems and for placement of power electronic actuators in a model of the European power grid.Comment: 7 pages, 2 figures; submitted to the 2014 IEEE Conference on Decision and Contro

Who Benefits from Obtaining a GED? Evidence from High School and Beyond

This paper examines the value of the GED credential and the conventional high school diploma in explaining the earnings of 27-year-old males in the early 1990s. The data base is the High School & Beyond sophomore cohort. We replicate the basic findings of prior studies that implicitly assume the labor market value of the GED credential does not depend on the skills with which dropouts left school. We show that these average effects mask a more complicated pattern. Obtaining a GED is associated with higher earnings at age 27 for those male dropouts who had very weak cognitive skills as tenth graders, but not for those who had stronger cognitive skills as tenth graders.

Do the Cognitive Skills of School Dropouts Matter in the Labor Market?

Does the U.S. labor market reward cognitive skill differences among high school dropouts, the members of the labor force with the least educational attainments? This paper reports the results of an exploration of this question, using a new data set that provides information on the universe of dropouts who last attempted the GED exams in Florida and New York between 1984 and 1990. The design of the sample reduces variation in unmeasured variables such as motivation that are correlated with cognitive skills. We examine the labor market returns to basic cognitive skills as measured by GED test scores. We explore whether the returns differ by gender and race. The results indicate quite large earnings returns to cognitive skills for both male and female dropouts, and for white and non-white dropouts. The earnings payoff to skills increases with age.

On Submodularity and Controllability in Complex Dynamical Networks

Controllability and observability have long been recognized as fundamental structural properties of dynamical systems, but have recently seen renewed interest in the context of large, complex networks of dynamical systems. A basic problem is sensor and actuator placement: choose a subset from a finite set of possible placements to optimize some real-valued controllability and observability metrics of the network. Surprisingly little is known about the structure of such combinatorial optimization problems. In this paper, we show that several important classes of metrics based on the controllability and observability Gramians have a strong structural property that allows for either efficient global optimization or an approximation guarantee by using a simple greedy heuristic for their maximization. In particular, the mapping from possible placements to several scalar functions of the associated Gramian is either a modular or submodular set function. The results are illustrated on randomly generated systems and on a problem of power electronic actuator placement in a model of the European power grid.Comment: Original arXiv version of IEEE Transactions on Control of Network Systems paper (Volume 3, Issue 1), with a addendum (located in the ancillary documents) that explains an error in a proof of the original paper and provides a counterexample to the corresponding resul