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All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

Multidimensional indexing structure for use with linear optimization queries

Linear optimization queries, which usually arise in various decision support and resource planning applications, are queries that retrieve top N data records (where N is an integer greater than zero) which satisfy a specific optimization criterion. The optimization criterion is to either maximize or minimize a linear equation. The coefficients of the linear equation are given at query time. Methods and apparatus are disclosed for constructing, maintaining and utilizing a multidimensional indexing structure of database records to improve the execution speed of linear optimization queries. Database records with numerical attributes are organized into a number of layers and each layer represents a geometric structure called convex hull. Such linear optimization queries are processed by searching from the outer-most layer of this multi-layer indexing structure inwards. At least one record per layer will satisfy the query criterion and the number of layers needed to be searched depends on the spatial distribution of records, the query-issued linear coefficients, and N, the number of records to be returned. When N is small compared to the total size of the database, answering the query typically requires searching only a small fraction of all relevant records, resulting in a tremendous speedup as compared to linearly scanning the entire dataset.

Bergman, Lawrence David↗
NASA NTRS2013

Powered Descent Guidance with General Thrust-Pointing Constraints

The Powered Descent Guidance (PDG) algorithm and software for generating Mars pinpoint or precision landing guidance profiles has been enhanced to incorporate thrust-pointing constraints. Pointing constraints would typically be needed for onboard sensor and navigation systems that have specific field-of-view requirements to generate valid ground proximity and terrain-relative state measurements. The original PDG algorithm was designed to enforce both control and state constraints, including maximum and minimum thrust bounds, avoidance of the ground or descent within a glide slope cone, and maximum speed limits. The thrust-bound and thrust-pointing constraints within PDG are non-convex, which in general requires nonlinear optimization methods to generate solutions. The short duration of Mars powered descent requires guaranteed PDG convergence to a solution within a finite time; however, nonlinear optimization methods have no guarantees of convergence to the global optimal or convergence within finite computation time. A lossless convexification developed for the original PDG algorithm relaxed the non-convex thrust bound constraints. This relaxation was theoretically proven to provide valid and optimal solutions for the original, non-convex problem within a convex framework. As with the thrust bound constraint, a relaxation of the thrust-pointing constraint also provides a lossless convexification that ensures the enhanced relaxed PDG algorithm remains convex and retains validity for the original nonconvex problem. The enhanced PDG algorithm provides guidance profiles for pinpoint and precision landing that minimize fuel usage, minimize landing error to the target, and ensure satisfaction of all position and control constraints, including thrust bounds and now thrust-pointing constraints.

Carson, John M., III↗
NASA NTRS2007

Optical Design of a Compact Imaging Spectrometer for Planetary Mineralogy

We present the design of a compact, wide-angle pushbroom imaging spectrometer suitable for exploration of solar system bodies from low orbit. The spectrometer is based on a single detector array with a broadband response that covers the range 400 to 3000 nm and provides a spectral sampling of 10 nm. The telescope has a 24-deg field of view with 600 spatially resolved elements (detector pixels). A specially designed convex diffraction grating permits optimization of the signal-to-noise ratio through the entire spectral band. Tolerances and design parameters permit the achievement of high uniformity of response through field and wavelength. The spectrometer performance is evaluated in terms of predicted spectral and spatial response functions and from the point of view of minimizing their variation through field and wavelength. The design serves as an example for illustrating the design principles specific to this type of system.

space optics↗
NASA NTRSDate not supplied

Interval Predictor Models for Robust System Identification

This paper proposes a framework for the identification and uncertainty quantification of plant models according to multivariable data. The only restriction imposed upon such models is for their outputs to depend continuously on their parameters. An Interval Predictor Model (IPM) prescribes the parameters of a computational model as a path-connected set thereby making each predicted output an interval-valued function of its inputs. The formulation proposed seeks the parameter set for which the predicted outputs tightly enclose the data. This set, which is modeled as a semi-algebraic set of low-degree polynomials, enables the characterization of possibly strong parameter dependencies commonly found in practice. This uncertainty characterization makes the resulting plant model amenable to robust control approaches using polynomial optimization. Furthermore, we use non-convex scenario theory to assess the reliability of the resulting IPM. This assessment yields a distribution-free upper bound on the probability that future data will fall outside the predicted intervals.

interval↗
NASA NTRS2002

Comparing a Coevolutionary Genetic Algorithm for Multiobjective Optimization

We present results from a study comparing a recently developed coevolutionary genetic algorithm (CGA) against a set of evolutionary algorithms using a suite of multiobjective optimization benchmarks. The CGA embodies competitive coevolution and employs a simple, straightforward target population representation and fitness calculation based on developmental theory of learning. Because of these properties, setting up the additional population is trivial making implementation no more difficult than using a standard GA. Empirical results using a suite of two-objective test functions indicate that this CGA performs well at finding solutions on convex, nonconvex, discrete, and deceptive Pareto-optimal fronts, while giving respectable results on a nonuniform optimization. On a multimodal Pareto front, the CGA finds a solution that dominates solutions produced by eight other algorithms, yet the CGA has poor coverage across the Pareto front.

Lohn, Jason D.↗
NASA NTRS1963

Mathematical Optimization Techniques

The papers collected in this volume were presented at the Symposium on Mathematical Optimization Techniques held in the Santa Monica Civic Auditorium, Santa Monica, California, on October 18-20, 1960. The objective of the symposium was to bring together, for the purpose of mutual education, mathematicians, scientists, and engineers interested in modern optimization techniques. Some 250 persons attended. The techniques discussed included recent developments in linear, integer, convex, and dynamic programming as well as the variational processes surrounding optimal guidance, flight trajectories, statistical decisions, structural configurations, and adaptive control systems. The symposium was sponsored jointly by the University of California, with assistance from the National Science Foundation, the Office of Naval Research, the National Aeronautics and Space Administration, and The RAND Corporation, through Air Force Project RAND.

Bellman, R.↗
NASA NTRS2012

Lossless Convexification of Control Constraints for a Class of Nonlinear Optimal Control Problems

In this paper we consider a class of optimal control problems that have continuous-time nonlinear dynamics and nonconvex control constraints. We propose a convex relaxation of the nonconvex control constraints, and prove that the optimal solution to the relaxed problem is the globally optimal solution to the original problem with nonconvex control constraints. This lossless convexification enables a computationally simpler problem to be solved instead of the original problem. We demonstrate the approach in simulation with a planetary soft landing problem involving a nonlinear gravity field.

planetary soft landing↗
NASA NTRS1991

Integration of mechanism and control for large-angle slew maneuvers of flexible structures

A rolling contact noncircular gear system is applied to assist a desired controller in the slewing of a flexible space structure. The varying gear ratio in cooperation with the controller results in lower feedback gains at the controller, as well as considerably reducing flexural vibrations of the space structure. The noncircular gears consist of a pair of convex noncircular cylinders with specially designed profiles that are synthesized in conjunction with the optimal controller gains for minimizing the flexural vibrations of flexible structure during a slew maneuver. Convexity of the cylindrical profiles for this noncircular gear device must be ensured to maintain rolling contact between the two cylinders. Simulations of slewing control tasks for two kinds of flexible space structures, such as a planar flexible beam and the planar articulated flexible beams, are presented.

Chew, Meng-Sang↗
NASA NTRS1986

Optimal block cosine transform image coding for noisy channels

The two dimensional block transform coding scheme based on the discrete cosine transform was studied extensively for image coding applications. While this scheme has proven to be efficient in the absence of channel errors, its performance degrades rapidly over noisy channels. A method is presented for the joint source channel coding optimization of a scheme based on the 2-D block cosine transform when the output of the encoder is to be transmitted via a memoryless design of the quantizers used for encoding the transform coefficients. This algorithm produces a set of locally optimum quantizers and the corresponding binary code assignment for the assumed transform coefficient statistics. To determine the optimum bit assignment among the transform coefficients, an algorithm was used based on the steepest descent method, which under certain convexity conditions on the performance of the channel optimized quantizers, yields the optimal bit allocation. Comprehensive simulation results for the performance of this locally optimum system over noisy channels were obtained and appropriate comparisons against a reference system designed for no channel error were rendered.

Vaishampayan, V.↗
NASA NTRS1990

Optimal block cosine transform image coding for noisy channels

The two dimensional block transform coding scheme based on the discrete cosine transform was studied extensively for image coding applications. While this scheme has proven to be efficient in the absence of channel errors, its performance degrades rapidly over noisy channels. A method is presented for the joint source channel coding optimiaation of a scheme based on the 2-D block cosine transorm when the output of the encoder is to be transmitted via a memoryless design of the quantizers used for encoding the transform coefficients. This algorithm produces a set of locally optimum quantizers and the corresponding binary code assignment for the assumed transform coefficient statistics. To determine the optimum bit assignment among the transform coefficients, an algorithm was used based on the steepest descent method, which under certain convexity conditions on the performance of the channel optimized quantizers, yields the optimal bit allocation. Comprehensive simulation results for the performance of this locally optimum system over noise channels were obtained and appropriate comparisons against a reference system designed for no channel error were rendered.

Vaishampayan, Vinay A.↗
NASA NTRS1986

Existence of the time optimal control for robotic manipulators

Using Filipov's Theorem, it is shown that the conditions oif nonfinite escape of trajectories, reachability, and convexity of the dynamics over all admissible controls are needed for the existence of a time optimal solution for the robotic equation. With a lower bound for the finite-escape time established using a Liapunov approach, and an upper bound for the time to reach the target established using the exact linearization idea, a single inequality is found which is closely related to the coriolis and the centrifugal terms, the absence of which implies that the domain of existence of the optimal solution can be made arbitrarily large with a large torque constraint. As the work space is finite, this is essentially a global result in practical situations.

Wen, J.↗
NASA NTRS2014

Interval Predictor Models with a Formal Characterization of Uncertainty and Reliability

This paper develops techniques for constructing empirical predictor models based on observations. By contrast to standard models, which yield a single predicted output at each value of the model's inputs, Interval Predictors Models (IPM) yield an interval into which the unobserved output is predicted to fall. The IPMs proposed prescribe the output as an interval valued function of the model's inputs, render a formal description of both the uncertainty in the model's parameters and of the spread in the predicted output. Uncertainty is prescribed as a hyper-rectangular set in the space of model's parameters. The propagation of this set through the empirical model yields a range of outputs of minimal spread containing all (or, depending on the formulation, most) of the observations. Optimization-based strategies for calculating IPMs and eliminating the effects of outliers are proposed. Outliers are identified by evaluating the extent by which they degrade the tightness of the prediction. This evaluation can be carried out while the IPM is calculated. When the data satisfies mild stochastic assumptions, and the optimization program used for calculating the IPM is convex (or, when its solution coincides with the solution to an auxiliary convex program), the model's reliability (that is, the probability that a future observation would be within the predicted range of outputs) can be bounded rigorously by a non-asymptotic formula.

Crespo, Luis G.↗
NASA NTRS1990

Random search optimization based on genetic algorithm and discriminant function

The general problem of optimization with arbitrary merit and constraint functions, which could be convex, concave, monotonic, or non-monotonic, is treated using stochastic methods. To improve the efficiency of the random search methods, a genetic algorithm for the search phase and a discriminant function for the constraint-control phase were utilized. The validity of the technique is demonstrated by comparing the results to published test problem results. Numerical experimentation indicated that for cases where a quick near optimum solution is desired, a general, user-friendly optimization code can be developed without serious penalties in both total computer time and accuracy.

Kiciman, M. O.↗
NASA NTRS1990

Global optimization methods for engineering design

The problem is to find a global minimum for the Problem P. Necessary and sufficient conditions are available for local optimality. However, global solution can be assured only under the assumption of convexity of the problem. If the constraint set S is compact and the cost function is continuous on it, existence of a global minimum is guaranteed. However, in view of the fact that no global optimality conditions are available, a global solution can be found only by an exhaustive search to satisfy Inequality. The exhaustive search can be organized in such a way that the entire design space need not be searched for the solution. This way the computational burden is reduced somewhat. It is concluded that zooming algorithm for global optimizations appears to be a good alternative to stochastic methods. More testing is needed; a general, robust, and efficient local minimizer is required. IDESIGN was used in all numerical calculations which is based on a sequential quadratic programming algorithm, and since feasible set keeps on shrinking, a good algorithm to find an initial feasible point is required. Such algorithms need to be developed and evaluated.

Arora, Jasbir S.↗