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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 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Guaranteed robustness properties of multivariable nonlinear stochastic optimal regulators

The robustness of optimal regulators for nonlinear, deterministic and stochastic, multi-input dynamical systems is studied under the assumption that all state variables can be measured. It is shown that, under mild assumptions, such nonlinear regulators have a guaranteed infinite gain margin; moreover, they have a guaranteed 50 percent gain reduction margin and a 60 degree phase margin, in each feedback channel, provided that the system is linear in the control and the penalty to the control is quadratic, thus extending the well-known properties of LQ regulators to nonlinear optimal designs. These results are also valid for infinite horizon, average cost, stochastic optimal control problems.

Tsitsiklis, J. N.↗
NASA NTRS1996

An optimized index of human cardiovascular adaptation to simulated weightlessness

Prolonged exposure to weightlessness is known to produce a variety of cardiovascular changes, some of which may influence the astronaut's performance during a mission. In order to find a reliable indicator of cardiovascular adaptation to weightlessness, we analyzed data from nine male subjects after a 24-hour period of normal activity and after a period of simulated weightlessness produced by two hours in a launch position followed by 20 hours of 6 degrees head-down tilt plus pharmacologically induced diuresis (furosemide). Heart rate, arterial pressure, thoracic fluid index, and radial flow were analyzed. Autoregressive spectral estimation and decomposition were used to obtain the spectral components of each variable from the subjects in the supine position during pre- and post-simulated weightlessness. We found a significant decrease in heart rate power and an increase in thoracic fluid index power in the high frequency region (0.2-0.45 Hz) and significant increases in radial flow and arterial pressure powers in the low frequency region (<0.2 Hz) in response to simulated weightlessness. However, due to the variability among subjects, any single variable appeared limited as a dependable index of cardiovascular adaptation to weightlessness. The backward elimination algorithm was then used to select the best discriminatory features from these spectral components. Fisher's linear discriminant and Bayes' quadratic discriminant were used to combine the selected features to obtain an optimal index of adaptation to simulated weightlessness. Results showed that both techniques provided improved discriminant performance over any single variable and thus have the potential for use as an index to track adaptation and prescribe countermeasures to the effects of weightlessness.

NASA Discipline Number 14-10↗
NASA NTRS1990

Exponential approximations in optimal design

One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis.

Belegundu, A. D.↗
NASA NTRS1986

Unified control/structure design and modeling research

To demonstrate the applicability of the control theory for distributed systems to large flexible space structures, research was focused on a model of a space antenna which consists of a rigid hub, flexible ribs, and a mesh reflecting surface. The space antenna model used is discussed along with the finite element approximation of the distributed model. The basic control problem is to design an optimal or near-optimal compensator to suppress the linear vibrations and rigid-body displacements of the structure. The application of an infinite dimensional Linear Quadratic Gaussian (LQG) control theory to flexible structure is discussed. Two basic approaches for robustness enhancement were investigated: loop transfer recovery and sensitivity optimization. A third approach synthesized from elements of these two basic approaches is currently under development. The control driven finite element approximation of flexible structures is discussed. Three sets of finite element basic vectors for computing functional control gains are compared. The possibility of constructing a finite element scheme to approximate the infinite dimensional Hamiltonian system directly, instead of indirectly is discussed.

Mingori, D. L.↗
DOE OSTI2024

Comparative Evaluation of Control-Oriented Heavy Duty Vehicle Air Drag Coefficient Models

Heavy-duty vehicles (HDVs) are a significant source of fuel consumption and greenhouse gas emissions, prompting solutions such as HDV platooning to mitigate these negative impacts through air drag reduction. The intervehicle distance in an HDV platoon needs to be carefully selected, such that the platoon-level energy efficiency and safety considerations can be well balanced. Underlying this problem lies in accurately modeling the relationship between HDV air drag coefficient and intervehicle distance. Through comprehensive evaluation and comparison, we analyze five control-oriented HDV air drag coefficient models, including the polynomial model, rational polynomial model, rational model, semi-quadratic model, and ridge model. Leveraging Scipy Curve-Fit toolbox and our previously compiled air drag coefficient datasets, we optimally identify the parameters inside each model. The calibrated models are then thoroughly evaluated via five complementary metrics. The comparison results reveal that the semi-quadratic model has the highest overall performance, while the widely adopted rational model only exhibits suboptimal performance.

Best, Micah↗
NASA NTRS1993

Optimal fixed-finite-dimensional compensator for Burgers' equation with unbounded input/output operators

The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction techniques in conjunction with linear quadratic Gaussian (LQG) theory. The approach used is based on the finite dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.

Burns, John A.↗
DOE OSTI2025

Surrogate modeling and optimization of the leaching process in a rare earth elements recovery plant

Critical minerals (CMs) and Rare Earth Elements (REEs) play a vital role in crucial infrastructure technologies such as renewable energy generation and batteries. Recovering them from waste materials has recently been found to significantly reduce environmental impact and supply chain costs related to these materials. In this work, we investigate surrogate modeling techniques aimed to simplify the modeling, simulation, and optimization of the leaching processes involved in CM and REE recovery flowsheets. As there is currently a lack of systematic studies on this topic, we perform extensive computational testing to ascertain which surrogate models are easier to construct and offer high predictive accuracy. Further, our results suggest that sparse quadratic models balance predictive accuracy and computational efficiency. Training and using these surrogates for global optimization of the leaching process requires two orders of magnitude fewer measurements and is up to four orders of magnitude faster than optimizing the original simulation using equation-oriented optimization or derivative-free optimization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1987

Linear quadratic stationkeeping on travelling ellipses

An automatic controller for Space Shuttle stationkeeping or formationkeeping is presented. The controller, which is a candidate for future on-orbit autopilot enhancement, uses a fuel 'optimized' limit cycle trajectory in a feedforward loop for precise control at nonequilibrium set points. Disturbance rejection is accomplished by a discrete time, linear quadratic regulator, which is employed for tracking of the feedforward model. Feedback gain selection is done to provide good limit cycling performance and low fuel consumption. Velocity correlations are carried out by use of a pseudo 6 degree-of-freedom jet selection scheme. Results indicate that 20 ft precision can be achieved using current sensors.

Adams, Neil J.↗
NASA NTRS1991

Closed-form solutions for linear regulator design of mechanical systems including optimal weighting matrix selection

Vibration in modern structural and mechanical systems can be reduced in amplitude by increasing stiffness, redistributing stiffness and mass, and/or adding damping if design techniques are available to do so. Linear Quadratic Regulator (LQR) theory in modern multivariable control design, attacks the general dissipative elastic system design problem in a global formulation. The optimal design, however, allows electronic connections and phase relations which are not physically practical or possible in passive structural-mechanical devices. The restriction of LQR solutions (to the Algebraic Riccati Equation) to design spaces which can be implemented as passive structural members and/or dampers is addressed. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical system. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist.

Hanks, Brantley R.↗
DOE OSTI2014

Certification and the potential energy landscape

Typically, there is no guarantee that a numerical approximation obtained using standard nonlinear equation solvers is indeed an actual solution, meaning that it lies in the quadratic convergence basin. Instead, it may lie only in the linear convergence basin, or even in a chaotic region, and hence not converge to the corresponding stationary point when further optimization is attempted. In some cases, these non-solutions could be misleading. Proving that a numerical approximation will quadratically converge to a stationary point is termed certification. In this report, we provide details of how Smale's α-theory can be used to certify numerically obtained stationary points of a potential energy landscape, providing a mathematical proof that the numerical approximation does indeed correspond to an actual stationary point, independent of the precision employed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1984

Gain optimization with non-linear controls

An algorithm has been developed for the analysis and design of controls for non-linear systems. The technical approach is to use statistical linearization to model the non-linear dynamics of a system by a quasi-Gaussian model. 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 paper 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 non-linearity be considered in the analysis.

Slater, G. L.↗
DOE OSTI2016

Optimization-based mesh correction with volume and convexity constraints

Here, we consider the problem of finding a mesh such that 1) it is the closest, with respect to a suitable metric, to a given source mesh having the same connectivity, and 2) the volumes of its cells match a set of prescribed positive values that are not necessarily equal to the cell volumes in the source mesh. Also, this volume correction problem arises in important simulation contexts, such as satisfying a discrete geometric conservation law and solving transport equations by incremental remapping or similar semi-Lagrangian transport schemes. In this paper we formulate volume correction as a constrained optimization problem in which the distance to the source mesh defines an optimization objective, while the prescribed cell volumes, mesh validity and/or cell convexity specify the constraints. We solve this problem numerically using a sequential quadratic programming (SQP) method whose performance scales with the mesh size. To achieve scalable performance we develop a specialized multigrid-based preconditioner for optimality systems that arise in the application of the SQP method to the volume correction problem. Numerical examples illustrate the importance of volume correction, and showcase the accuracy, robustness and scalability of our approach.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1992

Microgravity vibration isolation: Optimal preview and feedback control

In order to achieve adequate low-frequency vibration isolation for certain space experiments an active control is needed, due to inherent passive-isolator limitations. Proposed here are five possible state-space models for a one-dimensional vibration isolation system with a quadratic performance index. The five models are subsets of a general set of nonhomogeneous state space equations which includes disturbance terms. An optimal control is determined, using a differential equations approach, for this class of problems. This control is expressed in terms of constant, Linear Quadratic Regulator (LQR) feedback gains and constant feedforward (preview) gains. The gains can be easily determined numerically. They result in a robust controller and offers substantial improvements over a control that uses standard LQR feedback alone.

Hampton, R. D.↗
NASA NTRS2012

Bi-Objective Optimal Control Modification Adaptive Control for Systems with Input Uncertainty

This paper presents a new model-reference adaptive control method based on a bi-objective optimal control formulation for systems with input uncertainty. A parallel predictor model is constructed to relate the predictor error to the estimation error of the control effectiveness matrix. In this work, we develop an optimal control modification adaptive control approach that seeks to minimize a bi-objective linear quadratic cost function of both the tracking error norm and predictor error norm simultaneously. The resulting adaptive laws for the parametric uncertainty and control effectiveness uncertainty are dependent on both the tracking error and predictor error, while the adaptive laws for the feedback gain and command feedforward gain are only dependent on the tracking error. The optimal control modification term provides robustness to the adaptive laws naturally from the optimal control framework. Simulations demonstrate the effectiveness of the proposed adaptive control approach.

Nguyen, Nhan T.↗
DOE OSTI2024

On Properties of Adjoint Systems for Evolutionary PDEs

We investigate the geometric structure of adjoint systems associated with evolutionary partial differential equations at the fully continuous, semi-discrete, and fully discrete levels and the relations between these levels. We show that the adjoint system associated with an evolutionary partial differential equation has an infinite-dimensional Hamiltonian structure, which is useful for connecting the fully continuous, semi-discrete, and fully discrete levels. We subsequently address the question of discretize-then-optimize versus optimize-then-discrete for both semi-discretization and time integration, by characterizing the commutativity of discretize-then-optimize methods versus optimize-then-discretize methods uniquely in terms of an adjoint-variational quadratic conservation law. For Galerkin semi-discretizations and one-step time integration methods in particular, we explicitly construct these commuting methods by using structure-preserving discretization techniques.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Quantum simulation of real-space dynamics

Quantum simulation is a prominent application of quantum computers. While there is extensive previous work on simulating finite-dimensional systems, less is known about quantum algorithms for real-space dynamics. We conduct a systematic study of such algorithms. In particular, we show that the dynamics of a d-dimensional Schrödinger equation with η particles can be simulated with gate complexity O ~ (ηdFpoly(log(g'/ϵ))), where ϵ is the discretization error, g' controls the higher-order derivatives of the wave function, and F measures the time-integrated strength of the potential. Compared to the best previous results, this exponentially improves the dependence on ϵ and g' from poly(g'/ϵ) to poly(log(g'/ϵ)) and polynomially improves the dependence on T and d, while maintaining best known performance with respect to η. For the case of Coulomb interactions, we give an algorithm using η 3 (d + η)Tpoly(log(ηdTg'/(Δϵ)))/Δ one- and two-qubit gates, and another using η 3 (4d) d/2 Tpoly(log(ηdTg'/(Δϵ)))/Δ one- and two-qubit gates and QRAM operations, where T is the evolution time and the parameter Δ regulates the unbounded Coulomb interaction. We give applications to several computational problems, including faster real-space simulation of quantum chemistry, rigorous analysis of discretization error for simulation of a uniform electron gas, and a quadratic improvement to a quantum algorithm for escaping saddle points in nonconvex optimization.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1974

On the application of deterministic optimization methods to stochastic control problems

A technique is presented by which deterministic optimization techniques, for example, the maximum principle of Pontriagin, can be applied to stochastic optimal control problems formulated around linear systems with Gaussian noises and general cost criteria. Using this technique, the stochastic nature of the problem is suppressed but for two expectation operations, the optimization being deterministic. The use of the technique in treating problems with quadratic and nonquadratic costs is illustrated.

Kramer, L. C.↗