26,607 research outputs found
An Optimal Control Theory for the Traveling Salesman Problem and Its Variants
We show that the traveling salesman problem (TSP) and its many variants may
be modeled as functional optimization problems over a graph. In this
formulation, all vertices and arcs of the graph are functionals; i.e., a
mapping from a space of measurable functions to the field of real numbers. Many
variants of the TSP, such as those with neighborhoods, with forbidden
neighborhoods, with time-windows and with profits, can all be framed under this
construct. In sharp contrast to their discrete-optimization counterparts, the
modeling constructs presented in this paper represent a fundamentally new
domain of analysis and computation for TSPs and their variants. Beyond its
apparent mathematical unification of a class of problems in graph theory, the
main advantage of the new approach is that it facilitates the modeling of
certain application-specific problems in their home space of measurable
functions. Consequently, certain elements of economic system theory such as
dynamical models and continuous-time cost/profit functionals can be directly
incorporated in the new optimization problem formulation. Furthermore, subtour
elimination constraints, prevalent in discrete optimization formulations, are
naturally enforced through continuity requirements. The price for the new
modeling framework is nonsmooth functionals. Although a number of theoretical
issues remain open in the proposed mathematical framework, we demonstrate the
computational viability of the new modeling constructs over a sample set of
problems to illustrate the rapid production of end-to-end TSP solutions to
extensively-constrained practical problems.Comment: 24 pages, 8 figure
Electricity from photovoltaic solar cells: Flat-Plate Solar Array Project final report. Volume VI: Engineering sciences and reliability
The Flat-Plate Solar Array (FSA) Project, funded by the U.S. Government and managed by the Jet Propulsion Laboratory, was formed in 1975 to develop the module/array technology needed to attain widespread terrestrial use of photovoltaics by 1985. To accomplish this, the FSA Project established and managed an Industry, University, and Federal Government Team to perform the needed research and development.
This volume of the series of final reports documenting the FSA Project deals with the Project's activities directed at developing the engineering technology base required to achieve modules that meet the functional, safety and reliability requirements of large-scale terrestrial photovoltaic systems applications. These activities included: (1) development of functional, safety, and reliability requirements for such applications; (2) development of the engineering analytical approaches, test techniques, and design solutions required to meet the requirements; (3) synthesis and procurement of candidate designs for test and evaluation; and (4) performance of extensive testing, evaluation, and failure analysis to define design shortfalls and, thus, areas requiring additional research and development.
During the life of the FSA Project, these activities were known by and included a variety of evolving organizational titles: Design and Test, Large-Scale Procurements, Engineering, Engineering Sciences, Operations, Module Performance and Failure Analysis, and at the end of the Project, Reliability and Engineering Sciences.
This volume provides both a summary of the approach and technical outcome of these activities and provides a complete Bibliography (Appendix A) of the published documentation covering the detailed accomplishments and technologies developed
Flat-plate solar array project. Volume 6: Engineering sciences and reliability
The Flat-Plate Solar Array (FSA) Project activities directed at developing the engineering technology base required to achieve modules that meet the functional, safety, and reliability requirements of large scale terrestrial photovoltaic systems applications are reported. These activities included: (1) development of functional, safety, and reliability requirements for such applications; (2) development of the engineering analytical approaches, test techniques, and design solutions required to meet the requirements; (3) synthesis and procurement of candidate designs for test and evaluation; and (4) performance of extensive testing, evaluation, and failure analysis of define design shortfalls and, thus, areas requiring additional research and development. A summary of the approach and technical outcome of these activities are provided along with a complete bibliography of the published documentation covering the detailed accomplishments and technologies developed
Instability of fixed, low-thrust drag compensation
FORCED drag compensation using continuous low-thrustpropulsion has been considered for satellites in low Earth orbit. This simple, but nonoptimal, scheme merely requires that the thrust vector is directed opposite to the drag vector and that the magnitude of the two are equal. In principle, the drag force acting on the spacecraft could be determined onboard using accurate accelerometers. However, for small, low-cost spacecraft such sensors may beunavailable. An alternative strategy would be to Ĺ˝ x the thrust magnitude equal to the expected air drag that would be experienced by the spacecraft. The thrust levelwould be periodically updated based on ground-based orbit determination. In this Engineering Note, it is shown that such a forced circular orbit with a Ĺ˝ fixed thrust levelis exponentially unstable for all physically reasonable atmosphere models
A Universal Birkhoff Theory for Fast Trajectory Optimization
Over the last two decades, pseudospectral methods based on Lagrange
interpolants have flourished in solving trajectory optimization problems and
their flight implementations. In a seemingly unjustified departure from these
highly successful methods, a new starting point for trajectory optimization is
proposed. This starting point is based on the recently-developed concept of
universal Birkhoff interpolants. The new approach offers a substantial
computational upgrade to the Lagrange theory in completely flattening the rapid
growth of the condition numbers from O(N2) to O(1), where N is the number of
grid points. In addition, the Birkhoff-specific primal-dual computations are
isolated to a well-conditioned linear system even for nonlinear, nonconvex
problems. This is part I of a two-part paper. In part I, a new theory is
developed on the basis of two hypotheses. Other than these hypotheses, the
theoretical development makes no assumptions on the choices of basis functions
or the selection of grid points. Several covector mapping theorems are proved
to establish the mathematical equivalence between direct and indirect Birkhoff
methods. In part II of this paper (with Proulx), it is shown that a select
family of Gegenbauer grids satisfy the two hypotheses required for the theory
to hold. Numerical examples in part II illustrate the power and utility of the
new theory
Derivation of Coordinate Descent Algorithms from Optimal Control Theory
Recently, it was posited that disparate optimization algorithms may be
coalesced in terms of a central source emanating from optimal control theory.
Here we further this proposition by showing how coordinate descent algorithms
may be derived from this emerging new principle. In particular, we show that
basic coordinate descent algorithms can be derived using a maximum principle
and a collection of max functions as "control" Lyapunov functions. The
convergence of the resulting coordinate descent algorithms is thus connected to
the controlled dissipation of their corresponding Lyapunov functions. The
operational metric for the search vector in all cases is given by the Hessian
of the convex objective function
Fast Mesh Refinement in Pseudospectral Optimal Control
Mesh refinement in pseudospectral (PS) optimal control is embarrassingly easy
--- simply increase the order of the Lagrange interpolating polynomial and
the mathematics of convergence automates the distribution of the grid points.
Unfortunately, as increases, the condition number of the resulting linear
algebra increases as ; hence, spectral efficiency and accuracy are lost in
practice. In this paper, we advance Birkhoff interpolation concepts over an
arbitrary grid to generate well-conditioned PS optimal control discretizations.
We show that the condition number increases only as in general, but
is independent of for the special case of one of the boundary points being
fixed. Hence, spectral accuracy and efficiency are maintained as increases.
The effectiveness of the resulting fast mesh refinement strategy is
demonstrated by using \underline{polynomials of over a thousandth order} to
solve a low-thrust, long-duration orbit transfer problem.Comment: 27 pages, 12 figures, JGCD April 201
Charge-Focusing Readout of Time Projection Chambers
Time projection chambers (TPCs) have found a wide range of applications in
particle physics, nuclear physics, and homeland security. For TPCs with
high-resolution readout, the readout electronics often dominate the price of
the final detector. We have developed a novel method which could be used to
build large-scale detectors while limiting the necessary readout area. By
focusing the drift charge with static electric fields, we would allow a small
area of electronics to be sensitive to particle detection for a much larger
detector volume. The resulting cost reduction could be important in areas of
research which demand large-scale detectors, including dark matter searches and
detection of special nuclear material. We present simulations made using the
software package Garfield of a focusing structure to be used with a prototype
TPC with pixel readout. This design should enable significant focusing while
retaining directional sensitivity to incoming particles. We also present first
experimental results and compare them with simulation.Comment: 5 pages, 17 figures, Presented at IEEE Nuclear Science Symposium 201
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