We consider the solution of nonlinear programs in the case where derivatives of the objective function and nonlinear constraints are unavailable. To solve such problems, we propose an adaptation of a method due to Conn, Gould, Sartenaer, and Toint that proceeds by approximately minimizing a succession of linearly constrained augmented Lagrangians. Our modification is to use a derivative-free generating set direct search algorithm to solve the linearly constrained subproblems. The stopping criterion proposed by Conn, Gould, Sartenaer and Toint for the approximate solution of the subproblems requires explicit knowledge of derivatives. Such information is presumed absent in the generating set search method we employ. Instead, we show that stationarity results for linearly constrained generating set search methods provide a derivative-free stopping criterion, based on a step-length control parameter, that is sufficient to preserve the convergence properties of the original augmented Lagrangian algorithm.
This document describes new advances in hybrid reachability techniques accomplished during the course of a one-year Truman Postdoctoral Fellowship. These techniques provide guarantees of safety in complex systems, which is especially important in high-risk, expensive, or safety-critical systems. My work focused on new approaches to two specific problems motivated by real-world issues in complex systems: (1) multi-objective controller synthesis, and (2) control for recovery from error. Regarding the first problem, a novel application of reachability analysis allowed controller synthesis in a single step to achieve (a) safety, (b) stability, and (c) prevent input saturation. By extending the state to include the input parameters, constraints for stability, saturation, and envelope protection are incorporated into a single reachability analysis. Regarding the second problem, a new approach to the problem of recovery provides (a) states from which recovery is possible, and (b) controllers to guide the system during a recovery maneuver from an error state to a safe state in minimal time. Results are computed in both problems on nonlinear models of single longitudinal aircraft dynamics and two-aircraft lateral collision avoidance dynamics.
The growth of the flute-type instability for a field-aligned plasma column immersed in a uniform magnetic field is studied. Particle-in-cell simulations are compared with a semi-analytic dispersion analysis of the drift cyclotron instability in cylindrical geometry with a Gaussian density profile in the radial direction. For the parameters considered here, the dispersion analysis gives a local maximum for the peak growth rates as a function of R/r{sub i}, where R is the Gaussian characteristic radius and r{sub i} is the ion gyroradius. The electrostatic and electromagnetic particle-in-cell simulation results give azimuthal and radial mode numbers that are in reasonable agreement with the dispersion analysis. The electrostatic simulations give linear growth rates that are in good agreement with the dispersion analysis results, while the electromagnetic simulations yield growth rate trends that are similar to the dispersion analysis but that are not in quantitative agreement. These differences are ascribed to higher initial field fluctuation levels in the electromagnetic field solver. Overall, the simulations allow the examination of both the linear and nonlinear evolution of the instability in this physical system up to and beyond the point of wave energy saturation. Keywords: Microinstabilities, Magnetic confinement and equilibrium, Particle-in-cell method.
This report provides relevant information and analysis to the Department of Homeland Security (DHS) that will assist DHS in determining how to meet the requirements of federal technology transfer legislation. These legal requirements are grouped into five categories: (1) establishing an Office of Research and Technology Applications, or providing the functions thereof; (2) information management; (3) enabling agreements with non-federal partners; (4) royalty sharing; and (5) invention ownership/obligations. These five categories provide the organizing framework for this study, which benchmarks other federal agencies/laboratories engaged in technology transfer/transition Four key agencies--the Department of Health & Human Services (HHS), the U.S. Department of Agriculture (USDA), the Department of Energy (DOE), and the Department of Defense (DoD)--and several of their laboratories have been surveyed. An analysis of DHS's mission needs for commercializing R&D compared to those agencies/laboratories is presented with implications and next steps for DHS's consideration. Federal technology transfer legislation, requirements, and practices have evolved over the decades as agencies and laboratories have grown more knowledgeable and sophisticated in their efforts to conduct technology transfer and as needs and opinions in the federal sector have changed with regards to what is appropriate. The need to address requirements in a fairly thorough manner has, therefore, resulted in a lengthy paper. There are two ways to find summary information. Each chapter concludes with a summary, and there is an overall ''Summary and Next Steps'' chapter on pages 57-60. For those readers who are unable to read the entire document, we recommend referring to these pages.