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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

Gain optimization with nonlinear controls

An algorithm has been developed for the analysis and design of controls for nonlinear systems. The technical approach is to use statistical linearization to model the nonlinear dynamics of a system. A covariance analysis is performed to determine the behavior of the dynamical system and a quadratic cost function. Expressions for the cost function and its derivatives are determined so that numerical optimization techniques can be applied to determine optimal feedback laws. The primary application for this report is centered about the design of controls for nominally linear systems but where the controls are saturated or limited by fixed constraints. The analysis is general however and numerical computation requires only that the specific nonlinearity be considered in the analysis.

Slater, G. L.↗
NASA NTRS1978

Research on an augmented Lagrangian penalty function algorithm for nonlinear programming

The augmented Lagrangian (ALAG) Penalty Function Algorithm for optimizing nonlinear mathematical models is discussed. The mathematical models of interest are deterministic in nature and finite dimensional optimization is assumed. A detailed review of penalty function techniques in general and the ALAG technique in particular is presented. Numerical experiments are conducted utilizing a number of nonlinear optimization problems to identify an efficient ALAG Penalty Function Technique for computer implementation.

Frair, L.↗
DOE OSTI2023

Recent Developments in Security-Constrained AC Optimal Power Flow: Overview of Challenge 1 in the ARPA-E Grid Optimization Competition

In “Recent Developments in Security-Constrained AC Optimal Power Flow: Overview of Challenge 1 in the ARPA-E Grid Optimization Competition,” we review the state of the art in practical algorithms for scheduling power-systems operations in the short term and the results of the recent competition organized by the U.S. Advanced Research Projects Agency–Energy. We explain the mixed-integer nonlinear formulation used in the competition for nonspecialists in electrical engineering, the context and organization of the competition, and the performance of competitors. We find that the collective approaches and results of competitors provide support for efforts to move nonlinear optimization techniques into industrial applications, as they have proven to be a robust and efficient alternative to current linear approximation techniques.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1988

Cooperative control of two arms in the transport of an inertial load in zero gravity

In designing a robot control system for dual arm configurations, the control engineer is faced with two challenges: to derive the equations of motion for a given situation, and to meet certain desired control requirements (for instance, minimum energy). The former may involve closed kinematic chains, such as the case when the two arms are grasping a common object. The latter usually involves nonlinear optimization. These issues are considered in the context of transporting an inertial load using two planar three-link arms. A generalized 'reduction transformation' is applied to the dynamics to remove the singularity in the system equations. A suboptimal minimum energy method is presented to reduce a difficult 12-state, six-control nonlinear optimization to two independent, nonconflicting suboptimizations. A simulation example is provided to illustrate the degree of energy reduction possible using the optimal arm torque distribution that was developed.

Carignan, Craig R.↗
NASA NTRS2017

Electric Field Conjugation in the Presence of Model Uncertainty

The Wide-Field Infrared Survey Telescope (WFIRST) is a 2.4-meter-diameter space telescope NASA program. The payload will include a coronagraph instrument (CGI). The CGI designs under development use deformable mirrors (DM) to create a point spread function (PSF) with a dark region around the obscured star object. Electric field conjugation (EFC) is an iterative nonlinear optimization procedure that uses measurements of the electric field at the image to determine the DM displacements to modify the PSF to create the region of high contrast in the image. EFC requires a numerical model of the coronagraph to calculate the Jacobian of the system, which is used, along with regularization, to solve for the DM displacements for each iteration of the nonlinear optimization. Ideally, the coronagraph is aligned and calibrated, and the calibration data are used in the numerical model for calculating the Jacobian. However, calibration and alignment measurements always contain uncertainty resulting in calibration error. Therefore, the Jacobian calculated from the numerical model is not an exact representation of the physical coronagraph, and the resulting DM solution for an EFC iteration does not have the exact impact on the electric field of the coronagraph as predicted by the EFC. The result is slow convergence, and, as will be shown, drives the use of more restrictive regularization. Using Monte Carlo trials, we investigate the effect of calibration error on EFC convergence and regulatization. Comparison to results from the High Contrast Imaging Testbed Hybrid Lyot Coronagraph are also presented.

Marx, David↗
NASA NTRS1989

Bilinear modeling and nonlinear estimation

New methods are illustrated for online nonlinear estimation applied to the lateral deflection of an elastic beam on board measurements of angular rates and angular accelerations. The development of the filter equations, together with practical issues of their numerical solution as developed from global linearization by nonlinear output injection are contrasted with the usual method of the extended Kalman filter (EKF). It is shown how nonlinear estimation due to gyroscopic coupling can be implemented as an adaptive covariance filter using off-the-shelf Kalman filter algorithms. The effect of the global linearization by nonlinear output injection is to introduce a change of coordinates in which only the process noise covariance is to be updated in online implementation. This is in contrast to the computational approach which arises in EKF methods arising by local linearization with respect to the current conditional mean. Processing refinements for nonlinear estimation based on optimal, nonlinear interpolation between observations are also highlighted. In these methods the extrapolation of the process dynamics between measurement updates is obtained by replacing a transition matrix with an operator spline that is optimized off-line from responses to selected test inputs.

Dwyer, Thomas A. W., III↗
DOE OSTI2024

Iterative methods in GPU-resident linear solvers for nonlinear constrained optimization

Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra methods are often inefficient. For example, methods for solving ill-conditioned linear systems have relied on conditional branching, which degrades performance on hardware accelerators such as graphical processing units (GPUs). To improve the efficiency of solving ill-conditioned systems, our computational strategy separates computations that are efficient on GPUs from those that need to run on traditional central processing units (CPUs). Our strategy maximizes the reuse of expensive CPU computations. Iterative methods, which thus far have not been broadly used for ill-conditioned linear systems, play an important role in our approach. In particular, we extend ideas from Arioli et al., (2007) to implement iterative refinement using inexact LU factors and flexible generalized minimal residual (FGMRES), with the aim of efficient performance on GPUs. In conclusion, we focus on solutions that are effective within broader application contexts, and discuss how early performance tests could be improved to be more predictive of the performance in a realistic environment.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

TAO Users Manual (Rev. 3.15)

The Toolkit for Advanced Optimization (TAO) focuses on the development of algorithms and software for the solution of large-scale optimization problems on high-performance architectures. Areas of interest include unconstrained and bound-constrained optimization, nonlinear least squares problems, optimization problems with partial differential equation constraints, and variational inequalities and complementarity constraints. The development of TAO was motivated by the scattered support for parallel computations and the lack of reuse of external toolkits in current optimization software. Our aim is to produce high-quality optimization software for computing environments ranging from workstations and laptops to massively parallel high-performance architectures. Our design decisions are strongly motivated by the challenges inherent in the use of large-scale distributed memory architectures and the reality of working with large, often poorly structured legacy codes for specific applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Realizing the Materials-Designed-To-Environments Promise of Additive Manufacturing Through a Fundamentally Different Approach to Optimization of Nonlinear Solid Mechanics Structures

Additive Manufacturing (AM) is expected to play a large role in the labs-wide goals of accelerating innovation and leading in modern engineering. More specifically, AM is seen as a key enabling technology for increasing the agility of nuclear deterrence and other national security applications involving complex coupled environments. However, the impact of AM on these initiatives has not been as wide-ranging as hoped because – despite its unique qualities – the focus has mostly been on detailed qualification to force AM components into pre-existing performance envelopes. This paradigm fundamentally precludes the novel possibilities afforded by the geometric and material flexibility of AM. In particular, the engineering of small-scale features to undergo buckling and contact can cause large geometric and symmetry changes which provide responsiveness to different environments. Despite almost a decade of observing such behavior, there exists no way to systematically design for AM to exploit it. Our goal for this project was to connect material design to multi-environment component performance by reconceptualizing how to design for AM to exploit the buckling and contact of small-scale features.

36 MATERIALS SCIENCE↗
NASA NTRS1966

Nonlinear studies, optimal control

Attitude control for earth satellite in elliptic orbit, linearization in attitude control, and computation of optimal controls by method based on second variations

LINEARIZATION↗
NASA NTRS1976

Gradient optimization and nonlinear control

The book represents an introduction to computation in control by an iterative, gradient, numerical method, where linearity is not assumed. The general language and approach used are those of elementary functional analysis. The particular gradient method that is emphasized and used is conjugate gradient descent, a well known method exhibiting quadratic convergence while requiring very little more computation than simple steepest descent. Constraints are not dealt with directly, but rather the approach is to introduce them as penalty terms in the criterion. General conjugate gradient descent methods are developed and applied to problems in control.

Hasdorff, L.↗
NASA NTRS1990

Aircraft design for mission performance using nonlinear multiobjective optimization methods

A new technique which converts a constrained optimization problem to an unconstrained one where conflicting figures of merit may be simultaneously considered was combined with a complex mission analysis system. The method is compared with existing single and multiobjective optimization methods. A primary benefit from this new method for multiobjective optimization is the elimination of separate optimizations for each objective, which is required by some optimization methods. A typical wide body transport aircraft is used for the comparative studies.

Dovi, Augustine R.↗
NASA NTRS2010

Comparison of Traditional Design Nonlinear Programming Optimization and Stochastic Methods for Structural Design

Structural design generated by traditional method, optimization method and the stochastic design concept are compared. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the merit function with constraints imposed on failure modes and an optimization algorithm is used to generate the solution. Stochastic design concept accounts for uncertainties in loads, material properties, and other parameters and solution is obtained by solving a design optimization problem for a specified reliability. Acceptable solutions were produced by all the three methods. The variation in the weight calculated by the methods was modest. Some variation was noticed in designs calculated by the methods. The variation may be attributed to structural indeterminacy. It is prudent to develop design by all three methods prior to its fabrication. The traditional design method can be improved when the simplified sensitivities of the behavior constraint is used. Such sensitivity can reduce design calculations and may have a potential to unify the traditional and optimization methods. Weight versus reliabilitytraced out an inverted-S-shaped graph. The center of the graph corresponded to mean valued design. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure. Weight can be reduced to a small value for a most failure-prone design. Probabilistic modeling of load and material properties remained a challenge.

Patnaik, Surya N.↗