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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Q-Law for Rapid Assessment of Low Thrust Cislunar Trajectories Via Automatic Differentiation

Q-Law is a Lyapunov-based control law used to determine optimal controls for a low thrust trajectory. One major issue with its use is the difficult derivatives re-quired for calculating optimal controls at a given time. In this paper, an implementation of Q-Law with automatic differentiation via a Python package called JAX is applied. With automatic differentiation, the difficult derivatives for Q-Law’s optimal controls are calculated with ease, and derivatives of final states with respect to Q-Law’s weights are found enabling gradient-based optimization of Q-Law for the first time. Different search and optimization methods for finding optimal weights are then compared using the LEO to GEO problem, and it was found that gradient-free methods like design of experiments and genetic algorithm produced the best results, but they took the longest time to get a solution, while the gradient-based method found a locally optimal result in a much faster time. Overall, the run time for a single propagation is manageable and well-suited for a mission designer to use as an initial guess generator for trajectory optimization, or for simple orbit transfer analysis.

Nathan Steffen↗
DOE OSTI2026

Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study

Neural scaling laws play a pivotal role in the performance of deep neural networks and have been observed in a wide range of tasks. However, a complete theoretical framework for understanding these scaling laws remains underdeveloped. In this paper, we explore the neural scaling laws for deep operator networks, which involve learning mappings between function spaces, with a focus on the Chen and Chen style architecture. These approaches, which include the popular Deep Operator Network (DeepONet), approximate the output functions using a linear combination of learnable basis functions and coefficients that depend on the input functions. We establish a theoretical framework to quantify the neural scaling laws by analyzing its approximation and generalization errors. We articulate the relationship between the approximation and generalization errors of deep operator networks and key factors such as network model size and training data size. Moreover, we address cases where input functions exhibit low-dimensional structures, allowing us to derive tighter error bounds. These results also hold for deep ReLU networks and other similar structures. Our results offer a partial explanation of the neural scaling laws in operator learning and provide a theoretical foundation for their applications.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1978

A simplified Mach number scaling law for helicopter rotor noise

Mach number scaling laws are derived for the rotational and the high-frequency broadband noise from helicopter rotors. The rotational scaling law is obtained directly from the theory of Lowson and Ollerhead (1969) by exploiting the properties of the dominant terms in the expression for the complex Fourier coefficients of sound radiation from a point source. The scaling law for the high-frequency broadband noise is obtained by assuming that the noise sources are acoustically compact and computing the instantaneous pressure due to an element on an airfoil where vortices are shed. Experimental results on the correlation lengths for stationary airfoils are extended to rotating airfoils. On the assumption that the correlation length varies as the boundary layer displacement thickness, it is found that the Mach number scaling law contains a factor of Mach number raised to the exponent 5.8. Both scaling laws were verified by model tests.

Aravamudan, K. S.↗
NASA NTRS1979

Comparative study of flare control laws

A digital 3-D automatic control law was developed to achieve an optimal transition of a B-737 aircraft between various initial glid slope conditions and the desired final touchdown condition. A discrete, time-invariant, optimal, closed-loop control law presented for a linear regulator problem, was extended to include a system being acted upon by a constant disturbance. Two forms of control laws were derived to solve this problem. One method utilized the feedback of integral states defined appropriately and augmented with the original system equations. The second method formulated the problem as a control variable constraint, and the control variables were augmented with the original system. The control variable constraint control law yielded a better performance compared to feedback control law for the integral states chosen.

Nadkarni, A. A.↗
NASA NTRS1979

Development of a digital guidance and control law for steep approach automatic landings using modern control techniques

The development of a digital automatic control law for a small jet transport to perform a steep final approach in automatic landings is reported along with the development of a steady-state Kalman filter used to provide smooth estimates to the control law. The control law performs the functions of localizer and glides capture, localizer and glideslope track, decrab, and place. The control law uses the microwave landing system position data, and aircraft body-mounted accelerators, attitude and attitude rate information. The results obtained from a digital simulation of the aircraft dynamics, wind conditions, and sensor noises using the control law and filter developed are described.

Halyo, N.↗
NASA NTRS1981

A method for obtaining reduced-order control laws for high-order systems using optimization techniques

A method of synthesizing reduced-order optimal feedback control laws for a high-order system is developed. A nonlinear programming algorithm is employed to search for the control law design variables that minimize a performance index defined by a weighted sum of mean-square steady-state responses and control inputs. An analogy with the linear quadractic Gaussian solution is utilized to select a set of design variables and their initial values. To improve the stability margins of the system, an input-noise adjustment procedure is used in the design algorithm. The method is applied to the synthesis of an active flutter-suppression control law for a wind tunnel model of an aeroelastic wing. The reduced-order controller is compared with the corresponding full-order controller and found to provide nearly optimal performance. The performance of the present method appeared to be superior to that of two other control law order-reduction methods. It is concluded that by using the present algorithm, nearly optimal low-order control laws with good stability margins can be synthesized.

Mukhopadhyay, V.↗
NASA NTRS1984

Feedback laws for fuel minimization for transport aircraft

The Theoretical Mechanics Branch has as one of its long-range goals to work toward solving real-time trajectory optimization problems on board an aircraft. This is a generic problem that has application to all aspects of aviation from general aviation through commercial to military. Overall interest is in the generic problem, but specific problems to achieve concrete results are examined. The problem is to develop control laws that generate approximately optimal trajectories with respect to some criteria such as minimum time, minimum fuel, or some combination of the two. These laws must be simple enough to be implemented on a computer that is flown on board an aircraft, which implies a major simplification from the two point boundary value problem generated by a standard trajectory optimization problem. In addition, the control laws allow for changes in end conditions during the flight, and changes in weather along a planned flight path. Therefore, a feedback control law that generates commands based on the current state rather than a precomputed open-loop control law is desired. This requirement, along with the need for order reduction, argues for the application of singular perturbation techniques.

Price, D. B.↗
NASA NTRS1984

Application of optimization techniques to the design of a flutter suppression control law for the DAST ARW-2

The design of a candidate flutter suppression (FS) control law for the symmetric degrees of freedom for the DAST ARW-2 aircraft is discussed. The results illustrate the application of several currently employed control law design techniques. Subsequent designs, obtained as the mathematical model of the ARW-2 is updated, are expected to employ similar methods and to provide a control law whose performance will be flight tested. This study represents one of the steps necessary to provide an assessment of the validity of applying current control law synthesis and analysis techniques in the design of actively controlled aircraft. Mathematical models employed in the control law design and evaluation phases are described. The control problem is specified by presenting the flutter boundary predicted for the uncontrolled aircraft and by defining objectives and constraints that the controller should satisfy. A full-order controller is obtained by using Linear Quadratic Gaussian (LQG) techniques. The process of obtaining an implementable reduced-order controller is described. One example is also shown in which constrained optimization techniques are utilized to explicitly include robustness criteria within the design algorithm.

Adams, W. M., Jr.↗
NASA NTRS1987

Impact crater scaling laws

Impact craters are numerous on planetary bodies and furnish important information about the composition and past histories of those bodies. The interpretation of that information requires knowledge about the fundamental aspects of impact cratering mechanics. Since the typical conditions of impacts are at a size scale and velocity far in excess of experimental capabilities, direct simulations are precluded. Therefore, one must rely on extrapolation from experiments of relatively slow impacts of very small bodies, using physically based scaling laws, or must study the actual cases of interest using numerical code solutions of the fundamental physical laws that govern these processes. A progress report is presented on research on impact cratering scaling laws, on numerical studies that were designed to investigate those laws, and on various applications of the scaling laws developed by the author and his colleagues. These applications are briefly reviewed.

Holsapple, K. A.↗
NASA NTRS1988

Semi-discrete approximations to nonlinear systems of conservation laws; consistency and L(infinity)-stability imply convergence

A convergence theory for semi-discrete approximations to nonlinear systems of conservation laws is developed. It is shown, by a series of scalar counter-examples, that consistency with the conservation law alone does not guarantee convergence. Instead, a notion of consistency which takes into account both the conservation law and its augmenting entropy condition is introduced. In this context it is concluded that consistency and L(infinity)-stability guarantee for a relevant class of admissible entropy functions, that their entropy production rate belongs to a compact subset of H(loc)sup -1 (x,t). One can now use compensated compactness arguments in order to turn this conclusion into a convergence proof. The current state of the art for these arguments includes the scalar and a wide class of 2 x 2 systems of conservation laws. The general framework of the vanishing viscosity method is studied as an effective way to meet the consistency and L(infinity)-stability requirements. How this method is utilized to enforce consistency and stability for scalar conservation laws is shown. In this context we prove, under the appropriate assumptions, the convergence of finite difference approximations (e.g., the high resolution TVD and UNO methods), finite element approximations (e.g., the Streamline-Diffusion methods) and spectral and pseudospectral approximations (e.g., the Spectral Viscosity methods).

Tadmor, Eitan↗
NASA NTRS1988

Results of an integrated structure-control law design sensitivity analysis

Next generation air and space vehicle designs are driven by increased performance requirements, demanding a high level of design integration between traditionally separate design disciplines. Interdisciplinary analysis capabilities have been developed, for aeroservoelastic aircraft and large flexible spacecraft control for instance, but the requisite integrated design methods are only beginning to be developed. One integrated design method which has received attention is based on hierarchal problem decompositions, optimization, and design sensitivity analyses. This paper highlights a design sensitivity analysis method for Linear Quadratic Cost, Gaussian (LQG) optimal control laws, which predicts change in the optimal control law due to changes in fixed problem parameters using analytical sensitivity equations. Numerical results of a design sensitivity analysis for a realistic aeroservoelastic aircraft example are presented. In this example, the sensitivity of the optimally controlled aircraft's response to various problem formulation and physical aircraft parameters is determined. These results are used to predict the aircraft's new optimally controlled response if the parameter was to have some other nominal value during the control law design process. The sensitivity results are validated by recomputing the optimal control law for discrete variations in parameters, computing the new actual aircraft response, and comparing with the predicted response. These results show an improvement in sensitivity accuracy for integrated design purposes over methods which do not include changess in the optimal control law. Use of the analytical LQG sensitivity expressions is also shown to be more efficient that finite difference methods for the computation of the equivalent sensitivity information.

Gilbert, Michael G.↗
NASA NTRS1989

Results of an integrated structure/control law design sensitivity analysis

A design sensitivity analysis method for Linear Quadratic Cost, Gaussian (LQG) optimal control laws, which predicts change in the optimal control law due to changes in fixed problem parameters using analytical sensitivity equations is discussed. Numerical results of a design sensitivity analysis for a realistic aeroservoelastic aircraft example are presented. In this example, the sensitivity of the optimally controlled aircraft's response to various problem formulation and physical aircraft parameters is determined. These results are used to predict the aircraft's new optimally controlled response if the parameter was to have some other nominal value during the control law design process. The sensitivity results are validated by recomputing the optimal control law for discrete variations in parameters, computing the new actual aircraft response, and comparing with the predicted response. These results show an improvement in sensitivity accuracy for integrated design purposes over methods which do not include changes in the optimal control law. Use of the analytical LQG sensitivity expressions is also shown to be more efficient than finite difference methods for the computation of the equivalent sensitivity information.

Gilbert, Michael G.↗
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↗
NASA NTRS1990

Laser Atmospheric Wind Sounder (LAWS) phase 1. Volume 1: Executive summary

The laser atmospheric wind sounder (LAWS) will provide a new space based capability for the direct measurement of atmospheric winds in the troposphere. LAWS will make a major contribution toward advancing the understanding and prediction of the total Earth system and NASA's Earth Observing System (EOS) Program. LAWS is designed to measure a fundamental atmospheric parameter required to advance weather forecasting accuracies and investigate global climatic change. LAWS has a potential added benefit of providing (global) concentration profiles of large aerosols including visible and subvisible cirrus clouds, volcanic dust, smoke, and other pollutants. The objective of this Phase One study was to develop a LAWS concept and configuration. The instrument design is outlined in this first volume of three.

Source record↗
NASA NTRS1991

Control of a small working robot on a large flexible manipulator for suppressing vibrations: Development of a robust control law for flexible robot and it's stability analysis

Researchers developed a robust control law for slow motions for the accurate trajectory control of a flexible robot. The control law does not need larger velocity gains than position gains, which some researchers need to ensure the stability of a rigid robot. Initial experimentation for the Small Articulated Manipulator (SAM) shows that control laws that use smaller velocity gains are more robust to signal noise than the control laws that use larger velocity gains. Researchers analyzed the stability of the composite control law, the robust control for the slow motion, and the strain rate feedback for the fast control. The stability analysis was done by using a quadratic Liapunov function. Researchers found that the flexible motion of links could be controlled by relating the input force to the flexible signals which are sensed at the near tip of each link. The signals are contaminated by the time delayed input force. However, the effect of the time delayed input force can be reduced by giving a certain configuration to the SAM.

Soo, Han Lee↗
NASA NTRS1992

NASA STI Database, Aerospace Database and ARIN coverage of 'space law'

The space-law coverage provided by the NASA STI Database, the Aerospace Database, and ARIN is briefly described. Particular attention is given to the space law content of the two Databases and of ARIN, the NASA Thesauras space law terminology, space law publication forms, and the availability of the space law literature.

Buchan, Ronald L.↗
NASA NTRS1993

Power-law confusion: You say incremental, I say differential

Power-law distributions are commonly used to describe the frequency of occurrences of crater diameters, stellar masses, ring particle sizes, planetesimal sizes, and meteoroid masses to name a few. The distributions are simple, and this simplicity has led to a number of misstatements in the literature about the kind of power-law that is being used: differential, cumulative, or incremental. Although differential and cumulative power-laws are mathematically trivial, it is a hybrid incremental distribution that is often used and the relationship between the incremental distribution and the differential or cumulative distributions is not trivial. In many cases the slope of an incremental power-law will be nearly identical to the slope of the cumulative power-law of the same distribution, not the differential slope. The discussion that follows argues for a consistent usage of these terms and against the oft-made implicit claim that incremental and differential distributions are indistinguishable.

Colwell, Joshua E.↗
NASA NTRS1994

Vista/F-16 Multi-Axis Thrust Vectoring (MATV) control law design and evaluation

For the Multi-Axis Thrust Vectoring (MATV) program, a new control law was developed using multi-axis thrust vectoring to augment the aircraft's aerodynamic control power to provide maneuverability above the normal F-16 angle of attack limit. The control law architecture was developed using Lockheed Fort Worth's offline and piloted simulation capabilities. The final flight control laws were used in flight test to demonstrate tactical benefits gained by using thrust vectoring in air-to-air combat. Differences between the simulator aerodynamics data base and the actual aircraft aerodynamics led to significantly different lateral-directional flying qualities during the flight test program than those identified during piloted simulation. A 'dial-a-gain' flight test control law update was performed in the middle of the flight test program. This approach allowed for inflight optimization of the aircraft's flying qualities. While this approach is not preferred over updating the simulator aerodynamic data base and then updating the control laws, the final selected gain set did provide adequate lateral-directional flying qualities over the MATV flight envelope. The resulting handling qualities and the departure resistance of the aircraft allowed the 422nd_squadron pilots to focus entirely on evaluating the aircraft's tactical utility.

Zwerneman, W. D.↗