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Results for “Quadratic Optimization”

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 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Fuel Efficient Speed Optimization for Real-World Highway Cruising

This paper introduces an eco-driving highway cruising algorithm based on optimal control theory that is applied to a conventionally-powered connected and automated vehicle. Thanks to connectivity to the cloud and/or to infrastructure, speed limit and slope along the future route can be known with accuracy. This can in turn be used to compute the control variable trajectory that will minimize energy consumption without significantly impacting travel time. Automated driving is necessary to the implementation of this concept, because the chosen control variables (e.g., torque and gear) impact vehicle speed. An optimal control problem is built up where quadratic models are used for the powertrain. The optimization is solved by applying Pontryagin’s minimum principle, which reduces the problem to the minimization of a cost function with parameters called co-states. The proposed algorithm assumes piecewise constant slopes and speed limits, and it solves the transition vehicle speeds for each junction of such segments. In addition, a method to extract route information from digital maps is presented, which complies with the proposed optimization algorithm. The algorithms are evaluated in simulation, using Autonomie, a simulation tool for vehicle energy consumption modeling. The optimal control trajectory (e.g., torque, gear) is first computed offline. It is then applied in an open-loop fashion in online simulation, using a forward-looking model of the vehicle in Autonomie. Simulation results show over 8% fuel saving for two selected real-world routes.

Simulation and modeling, Optimization, Vehicle net↗
DOE OSTI2024

A multi-objective optimization model for cropland design considering profit, biodiversity, and ecosystem services

More sustainable agricultural methods are needed to alleviate the decreases in biodiversity and ecosystem services that have occurred because of industrial agriculture. One such method is the inclusion of alternative crops into croplands that can support biodiversity, reduce erosion and chemical runoff, and sequester carbon in the soil. However, the question of where such crops should be planted to balance competing economic and environmental objectives remains open. To this end, we develop a mixed-integer quadratically constrained program to optimize the layout of a cropland considering economic, biodiversity, greenhouse gas emissions, and water quality objectives. We include spatially varying fertilization as a decision variable in addition to crop establishment location. We further include the effect of core area and edges between different crops on biodiversity. To demonstrate the applicability of the model, we apply it to an example field, showing how the optimal cropland design changes as a decision-maker prioritizes different objectives and as edges have different impacts on biodiversity.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Grover-QAOA for 3-SAT: quadratic speedup, fair-sampling, and parameter clustering

Abstract The SAT problem is a prototypical NP-complete problem of fundamental importance in computational complexity theory with many applications in science and engineering; as such, it has long served as an essential benchmark for classical and quantum algorithms. This study shows numerical evidence for a quadratic speedup of the Grover Quantum Approximate Optimization Algorithm (G-QAOA) over random sampling for finding all solutions to 3-SAT (All-SAT) and Max-SAT problems. G-QAOA is less resource-intensive and more adaptable for these problems than Grover’s algorithm, and it surpasses conventional QAOA in its ability to sample all solutions. We show these benefits by classical simulations of many-round G-QAOA on thousands of random 3-SAT instances. We also observe G-QAOA advantages on the IonQ Aria quantum computer for small instances, finding that current hardware suffices to determine and sample all solutions. Interestingly, a single-angle-pair constraint that uses the same pair of angles at each G-QAOA round greatly reduces the classical computational overhead of optimizing the G-QAOA angles while preserving its quadratic speedup. We also find parameter clustering of the angles. The single-angle-pair protocol and parameter clustering significantly reduce obstacles to classical optimization of the G-QAOA angles.

Zhang, Zewen (ORCID:000000032258613X)↗
NASA NTRS1989

Digital robust control law synthesis using constrained optimization

Development of digital robust control laws for active control of high performance flexible aircraft and large space structures is a research area of significant practical importance. The flexible system is typically modeled by a large order state space system of equations in order to accurately represent the dynamics. The active control law must satisy multiple conflicting design requirements and maintain certain stability margins, yet should be simple enough to be implementable on an onboard digital computer. Described here is an application of a generic digital control law synthesis procedure for such a system, using optimal control theory and constrained optimization technique. A linear quadratic Gaussian type cost function is minimized by updating the free parameters of the digital control law, while trying to satisfy a set of constraints on the design loads, responses and stability margins. Analytical expressions for the gradients of the cost function and the constraints with respect to the control law design variables are used to facilitate rapid numerical convergence. These gradients can be used for sensitivity study and may be integrated into a simultaneous structure and control optimization scheme.

Mukhopadhyay, Vivekananda↗
DOE OSTI2014

TH-E-17A-05: Optimizing Four Dimensional Cone Beam Computed Tomography Projection Allocation to Respiratory Bins

Purpose: Four dimensional cone beam computed tomography (4DCBCT) is an emerging image guidance strategy but it can suffer from poor image quality. To avoid repeating scans it is beneficial to make the best use of the imaging data obtained. For conventional 4DCBCT the location and size of respiratory bins is fixed and projections are allocated to the respiratory bin within which it falls. Strictly adhering to this rule is unnecessary and can compromise image quality. In this study we optimize the size and location of respiratory bins and allow projections to be sourced from adjacent phases of the respiratory cycle. Methods: A mathematical optimization framework using mixed integer quadratic programming has been developed that determines when to source projections from adjacent respiratory bins and optimizes the size and location of the bins. The method, which we will call projection sharing, runs in under 2 seconds of CPU time. Five 4DCBCT datasets of stage III-IV lung cancer patients were used to test the algorithm. The standard deviation of the angular separation between projections (SD-A) and the standard deviation in the volume of the reconstructed fiducial gold coil (SD-V) were used as proxies to measure streaking artefacts and motion blur respectively. Results: The SD-A using displacement binning and projection sharing was 30%–50% smaller than conventional phase based binning and 59%–76% smaller than conventional displacement binning indicating more uniformly spaced projections and fewer streaking artefacts. The SD-V was 20–90% smaller when using projection sharing than using conventional phase based binning suggesting more uniform marker segmentation and less motion blur. Conclusion: Image quality was visibly and significantly improved with projection sharing. Projection sharing does not require any modifications to existing hardware and offers a more robust replacement to phase based binning, or, an option if phase based reconstruction is not of a suitable quality. This project is supported by an NHMRC Australia Fellowship and NHMRC project grant number 1034060.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1990

Piecewise linear approximation for hereditary control problems

This paper presents finite-dimensional approximations for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems, when a quadratic cost integral must be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in the case where the cost integral ranges over a finite time interval, as well as in the case where it ranges over an infinite time interval. The arguments in the last case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense.

Propst, Georg↗
DOE OSTI2017

Measuring galaxy cluster masses with CMB lensing using a Maximum Likelihood estimator: statistical and systematic error budgets for future experiments

We develop a Maximum Likelihood estimator (MLE) to measure the masses of galaxy clusters through the impact of gravitational lensing on the temperature and polarization anisotropies of the cosmic microwave background (CMB). We show that, at low noise levels in temperature, this optimal estimator outperforms the standard quadratic estimator by a factor of two. For polarization, we show that the Stokes Q/U maps can be used instead of the traditional E- and B-mode maps without losing information. We test and quantify the bias in the recovered lensing mass for a comprehensive list of potential systematic errors. Using realistic simulations, we examine the cluster mass uncertainties from CMB-cluster lensing as a function of an experiment’s beam size and noise level. We predict the cluster mass uncertainties will be 3 - 6% for SPT-3G, AdvACT, and Simons Array experiments with 10,000 clusters and less than 1% for the CMB-S4 experiment with a sample containing 100,000 clusters. The mass constraints from CMB polarization are very sensitive to the experimental beam size and map noise level: for a factor of three reduction in either the beam size or noise level, the lensing signal-to-noise improves by roughly a factor of two.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

SU-E-I-76: Matching Primary and Scattered X-Ray Spectra for Use in Calculating the Diagnostic Radiation Index of Protection

Purpose: Lightweight lead-free or lead-composite protective garments exploit k-edge interactions to attenuate scattered X-rays. Manufacturers specify the protective value of garments in terms of lead equivalence at a single kVp. This is inadequate, as the protection provided by such garments varies with radiation quality in different use conditions. We present a method for matching scattered X-ray spectra to primary X-ray spectra. The resulting primary spectra can be used to measure penetration through protective garments, and such measurements can be weighted and summed to determine a Diagnostic Radiation Index for Protection (DRIP). Methods: Scattered X-ray spectra from fluoroscopic procedures were modeled using Monte Carlo techniques in MCNP-X 2.7. Data on imaging geometry, operator position, patient size, and primary beam spectra were gathered from clinical fluoroscopy procedures. These data were used to generate scattered X-ray spectra resulting from procedural conditions. Technical factors, including kV and added filtration, that yielded primary X-ray spectra that optimally matched the generated scattered X-ray spectra were identified through numerical optimization using a sequential quadratic programming (SQP) algorithm. Results: The primary spectra generated with shape functions matched the relative flux in each bin of the scattered spectra within 5%, and half and quarter-value layers matched within 0.1%. The DRIP for protective garments can be determined by measuring the penetration through protective garments using the matched primary spectra, then calculating a weighted average according to the expected clinical use of the garment. The matched primary spectra are specified in terms of first and second half-value layers in aluminum and acrylic. Conclusion: Lead equivalence is inadequate for completely specifying the protective value of garments. Measuring penetration through a garment using full scatter conditions is very difficult. The primary spectra determined in this work allow for practical primary penetration measurements to be made with equipment readily available to clinical medical physicists.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2015

Non-Gaussian structure of B-mode polarization after delensing

The B-mode polarization of the cosmic microwave background on large scales has been considered as a probe of gravitational waves from the cosmic inflation. Ongoing and future experiments will, however, suffer from contamination due to the B-modes of non-primordial origins, one of which is the lensing induced B-mode polarization. Subtraction of the lensing B-modes, usually referred to as delensing, will be required for further improvement of detection sensitivity of the gravitational waves. In such experiments, knowledge of statistical properties of the B-modes after delensing is indispensable to likelihood analysis particularly because the lensing B-modes are known to be non-Gaussian. In this paper, we study non-Gaussian structure of the delensed B-modes on large scales, comparing it with that of the lensing B-modes. In particular, we investigate the power spectrum correlation matrix and the probability distribution function (PDF) of the power spectrum amplitude. Assuming an experiment in which the quadratic delensing is an almost optimal method, we find that delensing reduces correlations of the lensing B-mode power spectra between different multipoles, and that the PDF of the power spectrum amplitude is well described as a normal distribution function with a variance larger than that in the case of a Gaussian field. These features are well captured by an analytic model based on the 4th order Edgeworth expansion. As a consequence of the non-Gaussianity, the constraint on the tensor-to-scalar ratio after delensing is degraded within approximately a few percent, which depends on the multipole range included in the analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1987

Piecewise linear approximation for hereditary control problems

Finite dimensional approximations are presented for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems when a quadratic cost integral has to be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in case the cost integral ranges over a finite time interval as well as in the case it ranges over an infinite time interval. The arguments in the latter case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense. This feature is established using a vector-component stability criterion in the state space R(n) x L(2) and the favorable eigenvalue behavior of the piecewise linear approximations.

Propst, Georg↗
NASA NTRS1979

Analysis of integral controls in linear quadratic regulator design

The application of linear optimal control to the design of systems with integral control action on specified outputs is considered. Using integral terms in a quadratic performance index, an asymptotic analysis is used to determine the effect of variable quadratic weights on the eigenvalues and eigenvectors of the closed loop system. It is shown that for small integral terms the placement of integrator poles and gain calculation can be effectively decoupled from placement of the primary system eigenvalues. This technique is applied to the design of integral controls for a STOL aircraft outer loop guidance system.

Slater, G. L.↗
DOE OSTI2026

Implementing a unified solver for nonlinearly constrained optimization

SQP and interior-point methods (also referred to as Lagrange-Newton methods) typically share key algorithmic components, such as strategies for computing descent directions and mechanisms that promote global convergence. Building on this insight, we introduce a unifying framework with eight building blocks that abstracts the workflows of Lagrange-Newton methods. We then present Uno, a modular C++ solver that implements our unifying framework and allows the automatic combination of a wide range of strategies with no programming effort from the user. Uno is meant to (1) organize mathematical optimization strategies into a coherent hierarchy; (2) offer a wide range of efficient and robust methods that can be compared for a given instance; (3) enable researchers to experiment with novel optimization strategies; and (4) reduce the cost of development and maintenance of multiple optimization solvers. Uno’s software design allows user to compose new customized solvers for emerging optimization areas such as robust optimization or optimization problems with complementarity constraints, while building on reliable nonlinear optimization techniques. We demonstrate that Uno is highly competitive against state-of-the-art solvers filterSQP, IPOPT, SNOPT, MINOS, LANCELOT, LOQO, and CONOPT on a subset of 429 small problems from the CUTE collection. Uno is available as open-source software under the MIT license at https://github.com/cvanaret/Uno and via its C, Julia, Python, Fortran, and AMPL interfaces.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1979

Algebraic methods for the solution of some linear matrix equations

The characterization of polynomials whose zeros lie in certain algebraic domains (and the unification of the ideas of Hermite and Lyapunov) is the basis for developing finite algorithms for the solution of linear matrix equations. Particular attention is given to equations PA + A'P = Q (the Lyapunov equation) and P - A'PA = Q the (discrete Lyapunov equation). The Lyapunov equation appears in several areas of control theory such as stability theory, optimal control (evaluation of quadratic integrals), stochastic control (evaluation of covariance matrices) and in the solution of the algebraic Riccati equation using Newton's method.

Djaferis, T. E.↗
NASA NTRS1979

On reliable control system designs with and without feedback reconfigurations

This paper contains an overview of a theoretical framework for the design of reliable multivariable control systems, with special emphasis on actuator failures and necessary actuator redundancy levels. Using a linear model of the system, with Markovian failure probabilities and quadratic performance index, an optimal stochastic control problem is posed and solved. The solution requires the iteration of a set of highly coupled Riccati-like matrix difference equations; if these converge one has a reliable design; if they diverge, the design is unreliable, and the system design cannot be stabilized. In addition, it is shown that the existence of a stabilizing constant feedback gain and the reliability of its implementation is equivalent to the convergence properties of a set of coupled Riccati-like matrix difference equations. In summary, these results can be used for offline studies relating the open loop dynamics, required performance, actuator mean time to failure, and functional or identical actuator redundancy, with and without feedback gain reconfiguration strategies.

Birdwell, J. D.↗
NASA NTRS1980

Towards sub-optimal stochastic control of partially observable stochastic systems

A class of multidimensional stochastic control problems with noisy data and bounded controls encountered in aerospace design is examined. The emphasis is on suboptimal design, the optimality being taken in quadratic mean sense. To that effect the problem is viewed as a stochastic version of the Lurie problem known from nonlinear control theory. The main result is a separation theorem (involving a nonlinear Kalman-like filter) suitable for Lurie-type approximations. The theorem allows for discontinuous characteristics. As a byproduct the existence of strong solutions to a class of non-Lipschitzian stochastic differential equations in dimensions is proven.

Ruzicka, G. J.↗
NASA NTRS1980

Towards sub-optimal stochastic control of partially observable stochastic systems

The paper deals with a class of multidimensional stochastic control problems with noisy data and bounded controls encountered in aerospace design. The emphasis is on suboptimal design, the optimality being taken in quadratic mean sense. To that effect the problem is viewed as a stochastic version of the Lurie problem known from nonlinear control theory. The main result is a separation theorem (involving a nonlinear Kalman-like filter) suitable for Lurie-type approximations. The theorem allows for discontinuous characteristics. As a byproduct the existence of strong solutions to a class of non-Lipschitzian stochastic differential equations in n dimensions is proved.

Ruzicka, G. J.↗
NASA NTRS1988

On Hilbert-Schmidt norm convergence of Galerkin approximation for operator Riccati equations

An abstract approximation framework for the solution of operator algebraic Riccati equations is developed. The approach taken is based on a formulation of the Riccati equation as an abstract nonlinear operator equation on the space of Hilbert-Schmidt operators. Hilbert-Schmidt norm convergence of solutions to generic finite dimensional Galerkin approximations to the Riccati equation to the solution of the original infinite dimensional problem is argued. The application of the general theory is illustrated via an operator Riccati equation arising in the linear-quadratic design of an optimal feedback control law for a 1-D heat/diffusion equation. Numerical results demonstrating the convergence of the associated Hilbert-Schmidt kernels are included.

Rosen, I. G.↗