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Results for “Linear 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 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Model-following control for an oblique-wing aircraft

A variable-skew oblique wing offers a substantial aerodynamic performance advantage for aircraft missions that require both high efficiency in subsonic flight and supersonic dash or cruise. The most obvious characteristic of the oblique-wing concept is the asymmetry associated with wing-skew angle which results in significant aerodynamic and inertial cross-coupling between the aircraft longitudinal and lateral-directional axes. A technique for synthesizing a decoupling controller while providing the desired stability augmentation. The proposed synthesis procedure uses the cncept of explicit model following. Linear quadratic optimization techniques are used to design the linear feedback system. The effectiveness of the control laws developed in achieving the desired decoupling is illustrated for a given flight condition by application to linearized equations of motion, and also to the nonlinear equations of six degrees of freedom of motion with nonlinear aerodynamic data.

Alag, G. S.↗
NASA NTRS1986

Model-following control for an oblique-wing aircraft

A variable-skew oblique wing offers a substantial aerodynamic performance advantage for aircraft missions that require both high efficiency in subsonic flight and supersonic dash or cruise. The most obvious characteristic of the oblique-wing concept is the asymmetry associated with wing-skew angle which results in significant aerodynamic and inertial cross-coupling between the aircraft longitudinal and lateral-directional axes. This paper presents a technique for synthesizing a decoupling controller while providing the desired stability augmentation. The proposed synthesis procedure uses the concept of explicit model following. Linear quadratic optimization techniques are used to design the linear feedback system. The effectiveness of the control laws developed in achieving the desired decoupling is illustrated for a given flight condition by application to linearized equations of motion, and also to the nonlinear equations of six degrees of freedom of motion with nonlinear aerodynamic data.

Alag, G. S.↗
NASA NTRS1983

Orbit structure of Hamiltonian systems arising from Lie transformation group actions

This paper associates the Riccati group and its group action on linear-quadratic optimal control problems to the action of a Lie transformation group on a set of Hamiltonian matrices. In this Lie theoretic setting results are presented concerning the associated orbit structure and the structure of the group itself. These results are of importance in understanding the solution structure of matrix Riccati differential equations, and thus also of importance in linear-quadratic optimal control.

Garzia, M. R.↗
DOE OSTI2022

Optimal control to handle variations in moisture content and reactor in-feed rate

The variations in feedstock characteristics, such as moisture and particle size distribution, lead to an inconsistent flow of feedstock from the biomass pre-processing system to the reactor in-feed system. These inconsistencies result in low on-stream times at the reactor in-feed equipment. This research develops an optimal process control method for a biomass pre-processing system comprised of milling and densification operations to provide the consistent flow of feedstock to a reactor's throat. This method uses a mixed-integer optimization model to identify optimal bale sequencing, equipment in-feed rate, and buffer location and size in the biomass pre-processing system. This method, referred to as the hybrid process control (HPC), aims to maximize throughput over time. We compare HPC with a baseline feed forward process control. Our case study based on switchgrass finds that HPC reduces the variation of a reactor's feeding rate by up to 100% without increasing the operating cost of the biomass pre-processing system for biomass with moisture ranging from 10 to 25%. Additionally, HPC reduces the cost of processing biomass by 0.36%–2.22%, and reduces processing time by 0.35%-2.24%. Furthermore, a biorefinery can adapt HPC to achieve its design capacity.

09 BIOMASS FUELS↗
DOE OSTI2014

Direct leaf trajectory optimization for volumetric modulated arc therapy planning with sliding window delivery

Purpose: The authors propose a novel optimization model for volumetric modulated arc therapy (VMAT) planning that directly optimizes deliverable leaf trajectories in the treatment plan optimization problem, and eliminates the need for a separate arc-sequencing step. Methods: In this model, a 360° arc is divided into a given number of arc segments in which the leaves move unidirectionally. This facilitates an algorithm that determines the optimal piecewise linear leaf trajectories for each arc segment, which are deliverable in a given treatment time. Multileaf collimator constraints, including maximum leaf speed and interdigitation, are accounted for explicitly. The algorithm is customized to allow for VMAT delivery using constant gantry speed and dose rate, however, the algorithm generalizes to variable gantry speed if beneficial. Results: The authors demonstrate the method for three different tumor sites: a head-and-neck case, a prostate case, and a paraspinal case. The authors first obtain a reference plan for intensity modulated radiotherapy (IMRT) using fluence map optimization and 20 intensity-modulated fields in equally spaced beam directions, which is beyond the standard of care. Modeling the typical clinical setup for the treatment sites considered, IMRT plans using seven or nine beams are also computed. Subsequently, VMAT plans are optimized by dividing the 360° arc into 20 corresponding arc segments. Assuming typical machine parameters (a dose rate of 600 MU/min, and a maximum leaf speed of 3 cm/s), it is demonstrated that the optimized VMAT plans with 2–3 min delivery time are of noticeably better quality than the 7–9 beam IMRT plans. The VMAT plan quality approaches the quality of the 20-beam IMRT benchmark plan for delivery times between 3 and 4 min. Conclusions: The results indicate that high quality treatments can be delivered in a single arc with 20 arc segments if sufficient time is allowed for modulation in each segment.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2022

A data-driven linear formulation of the optimal demand response scheduling problem for an industrial air separation unit

Demand response (DR) has become a key element in balancing the power grid as the contribution of time-varying renewable power generation increases. Chemical plants are appealing candidates for DR programs as they offer large, concentrated and flexible loads. DR participation calls for frequent production rate changes over time scales that overlap with the dominant dynamics of the plant. Production scheduling should therefore consider the process dynamics explicitly. Here we present a data-driven approach for modelling the scheduling-relevant dynamics based on historical closed-loop operating data using autoregressive with extra inputs (ARX) models. We introduce a new, linear scheduling problem formulation based on the ARX representation, and demonstrate its implementation on an industrial air separation unit.

42 ENGINEERING↗
DOE OSTI2017

Optimizing Biorefinery Design and Operations via Linear Programming Models

The ability to assess and optimize economics of biomass resource utilization for the production of fuels, chemicals and power is essential for the ultimate success of a bioenergy industry. The team of authors, consisting of members from the National Renewable Energy Laboratory (NREL) and the Idaho National Laboratory (INL), has developed simple biorefinery linear programming (LP) models to enable the optimization of theoretical or existing biorefineries. The goal of this analysis is to demonstrate how such models can benefit the developing biorefining industry. It focuses on a theoretical multi-pathway, thermochemical biorefinery configuration and demonstrates how the biorefinery can use LP models for operations planning and optimization in comparable ways to the petroleum refining industry. Using LP modeling tools developed under U.S. Department of Energy's Bioenergy Technologies Office (DOE-BETO) funded efforts, the authors investigate optimization challenges for the theoretical biorefineries such as (1) optimal feedstock slate based on available biomass and prices, (2) breakeven price analysis for available feedstocks, (3) impact analysis for changes in feedstock costs and product prices, (4) optimal biorefinery operations during unit shutdowns / turnarounds, and (5) incentives for increased processing capacity. These biorefinery examples are comparable to crude oil purchasing and operational optimization studies that petroleum refiners perform routinely using LPs and other optimization models. It is important to note that the analyses presented in this article are strictly theoretical and they are not based on current energy market prices. The pricing structure assigned for this demonstrative analysis is consistent with $4 per gallon gasoline, which clearly assumes an economic environment that would favor the construction and operation of biorefineries. The analysis approach and examples provide valuable insights into the usefulness of analysis tools for maximizing the potential benefits of biomass utilization for production of fuels, chemicals and power.

09 BIOMASS FUELS↗
NASA NTRS2013

Adaptive Control for Linear Uncertain Systems with Unmodeled Dynamics Revisited via Optimal Control Modification

This paper presents the optimal control modification for linear uncertain plants. The Lyapunov analysis shows that the modification parameter has a limiting value depending on the nature of the uncertainty. The optimal control modification exhibits a linear asymptotic property that enables it to be analyzed in a linear time invariant framework for linear uncertain plants. The linear asymptotic property shows that the closed-loop plants in the limit possess a scaled input-output mapping. Using this property, we can derive an analytical closed-loop transfer function in the limit as the adaptive gain tends to infinity. The paper revisits the Rohrs counterexample problem that illustrates the nature of non-robustness of model-reference adaptive control in the presence of unmodeled dynamics. An analytical approach is developed to compute exactly the modification parameter for the optimal control modification that stabilizes the plant in the Rohrs counterexample. The linear asymptotic property is also used to address output feedback adaptive control for non-minimum phase plants with a relative degree 1.

Unmodeled Dynamics↗
NASA NTRS1972

Application of quadratic optimization to supersonic inlet control.

This paper describes the application of linear stochastic optimal control theory to the design of the control system for the air intake, the inlet, of a supersonic air-breathing propulsion system. The controls must maintain a stable inlet shock position in the presence of random airflow disturbances and prevent inlet unstart. Two different linear time invariant controllers are developed. One is designed to minimize a nonquadratic index, the expected frequency of inlet unstart, and the other is designed to minimize the mean square value of inlet shock motion. The quadratic equivalence principle is used to obtain a linear controller that minimizes the nonquadratic index. The two controllers are compared on the basis of unstart prevention, control effort requirements, and frequency response. It is concluded that while controls designed to minimize unstarts are desirable in that the index minimized is physically meaningful, computation time required is longer than for the minimum mean square shock position approach. The simpler minimum mean square shock position solution produced expected unstart frequency values which were not significantly larger than those of the nonquadratic solution.

Lehtinen, B.↗
NASA NTRS1978

ORACLS: A system for linear-quadratic-Gaussian control law design

A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.

Armstrong, E. S.↗
DOE OSTI2016

Sign Learning Kink-based (SiLK) Quantum Monte Carlo for molecular systems

The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ab initio ground state energies for multiple geometries of the H{sub 2}O, N{sub 2}, and F{sub 2} molecules. The method is based on Feynman’s path integral formulation of quantum mechanics and has two stages. The first stage is called the learning stage and reduces the well-known QMC minus sign problem by optimizing the linear combinations of Slater determinants which are used in the second stage, a conventional QMC simulation. The method is tested using different vector spaces and compared to the results of other quantum chemical methods and to exact diagonalization. Our findings demonstrate that the SiLK method is accurate and reduces or eliminates the minus sign problem.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1974

Optimal output feedback control of linear systems in presence of forcing and measurement noise

The problem of obtaining an optimal control law, which is constrained to be a linear feedback of the available measurements, for both continuous and discrete time linear systems subjected to additive white process noise and measurement noise was Necessary conditions are obtained for minimizing a quadratic performance function for both finite and infinite terminal time cases. The feedback gains are constrained to be time invariant for the infinite terminal time cases. For all the cases considered, algorithms are derived for generating sequences of feedback gain matrices which successively improve the performance function. A continuous time numerical example is included for the purpose of demonstration.

Joshi, S. M.↗
DOE OSTI2022

Computing x-ray absorption spectra from linear-response particles atop optimized holes

State specific orbital optimized density functional theory (OO-DFT) methods, such as restricted open-shell Kohn–Sham (ROKS), can attain semiquantitative accuracy for predicting x-ray absorption spectra of closed-shell molecules. OO-DFT methods, however, require that each state be individually optimized. In this Communication, we present an approach to generate an approximate core-excited state density for use with the ROKS energy ansatz, which is capable of giving reasonable accuracy without requiring state-specific optimization. Herein, this is achieved by fully optimizing the core-hole through the core-ionized state, followed by the use of electron-addition configuration interaction singles to obtain the particle level. This hybrid approach can be viewed as a DFT generalization of the static-exchange (STEX) method and can attain ~0.6 eV rms error for the K-edges of C–F through the use of local functionals, such as PBE and OLYP. This ROKS(STEX) approach can also be used to identify important transitions for full OO ROKS treatment and can thus help reduce the computational cost of obtaining OO-DFT quality spectra. ROKS(STEX), therefore, appears to be a useful technique for the efficient prediction of x-ray absorption spectra.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

GPU-resident sparse direct linear solvers for alternating current optimal power flow analysis

Integrating renewable resources within the transmission grid at a wide scale poses significant challenges for economic dispatch as it requires analysis with more optimization parameters, constraints, and sources of uncertainty. This motivates the investigation of more efficient computational methods, especially those for solving the underlying linear systems, which typically take more than half of the overall computation time. In this paper, we present our work on sparse linear solvers that take advantage of hardware accelerators, such as graphical processing units (GPUs), and improve the overall performance when used within economic dispatch computations. We treat the problems as sparse, which allows for faster execution but also makes the implementation of numerical methods more challenging. We present the first GPU-native sparse direct solver that can execute on both AMD and NVIDIA GPUs. We demonstrate significant performance improvements when using high-performance linear solvers within alternating current optimal power flow (ACOPF) analysis. Furthermore, we demonstrate the feasibility of getting significant performance improvements by executing the entire computation on GPU-based hardware. Finally, we identify outstanding research issues and opportunities for even better utilization of heterogeneous systems, including those equipped with GPUs.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Uncovering interpretable relationships in high-dimensional scientific data through function preserving projections

Abstract In many fields of science and engineering, we frequently encounter experiments or simulations datasets that describe the behavior of complex systems and uncovering human interpretable patterns between their inputs and outputs via exploratory data analysis is essential for building intuition and facilitating discovery. Often, we resort to 2D embeddings for examining these high-dimensional relationships (e.g. dimensionality reduction). However, most existing embedding methods treat the dimensions as coordinates for samples in a high-dimensional space, which fail to capture the potential functional relationships, and the few methods that do take function into consideration either only focus on linear patterns or produce non-linear embeddings that are hard to interpret. To address these challenges, we proposed function preserving projections (FPP), which construct 2D linear embeddings optimized to reveal interpretable yet potentially non-linear patterns between the domain and the range of a high-dimensional function. The intuition here is that humans are good at understanding potentially non-linear patterns in 2D but unable to interpret non-linear mapping from high-dimensional space to 2D. Therefore, we should restrict the projection to linear but not the pattern we are seeking. Using FPP on real-world datasets, one can obtain fundamentally new insights about high-dimensional relationships in extremely large datasets that could not be processed with existing dimension reduction methods.

97 MATHEMATICS AND COMPUTING↗