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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

An ideal MHD δW stability analysis that bypasses the Newcomb equation

In the following work, we demonstrate the efficacy of a Riccati δW ideal MHD stability analysis that bypasses the numerically intractable integration of the Newcomb equation. By transforming the linear Newcomb equation into a quadratic Riccati equation, an accurate and equivalent δW analysis is performed that is shown to enjoy some numerical advantages. Additionally, we demonstrate that the Riccati approach is better conditioned than its Newcomb counterpart at the magnetic axis, and we apply dynamical systems insights to examine its behavior at singular points. We further discuss the constraints involved in solving for the extremal admissible perturbations of a δW analysis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1976

Optimal control of spin stabilized spacecraft with telescoping appendages

The control of a spin-stabilized spacecraft consisting of a rigid central hub and one or two movable offset telescoping booms (with end masses) is considered. The equations of rotational motion are linearized about either of two desired final states. A control law for the boom and mass position is sought such that a quadratic cost functional involving the weighted components of angular velocity plus the control is minimized when the final time is unspecified and involves the solution of the matrix Riccati algebraic equation. For three-axis control more than one offset boom (orthogonal to each other) is required. For two-axis control with a single boom offset from a symmetrical hub, an analytic solution is obtained; when this system is used for nutation decay the time constant is one order of magnitude smaller than previously achieved using non-optimal control logic. For the general case results are obtained numerically.

Bainum, P. M.↗
NASA NTRS1976

Optimal control of spin-stabilized spacecraft with telescoping appendages

The control of a spin-stabilized spacecraft consisting of a rigid central hub and one or two movable offset telescoping booms (with end masses) is considered. The equations of rotational motion are linearized about either of two desired final states. A control law for the boom end mass position is sought such that a quadratic cost functional involving the weighted components of angular velocity plus the control is minimized when the final time is unspecified and involves the solution of the matrix Riccati algebraic equation. For three axis control more than one offset boom (orthogonal to each other) is required. For two-axis control with a single boom offset from a symmetrical hub, an analytic solution is obtained; when this system is used for nutation decay the time constant is one order of magnitude smaller than previously achieved using nonoptimal control logic. For the general case results are obtained numerically.

Bainum, P. M.↗
DOE OSTI2022

Parametric dependencies of resonant layer responses across linear, two-fluid, drift-MHD regimes

Non-axisymmetric magnetic fields arising in a tokamak either by external or internal perturbations can induce complex non-ideal MHD responses in their resonant surfaces while remaining ideally evolved elsewhere. This layer response can be characterized in a linear regime by a single parameter called the inner-layer Δ, which enables outer-layer matching and the prediction of torque balance to non-linear island regimes. In this work, we follow strictly one of the most comprehensive analytic treatments including two-fluid and drift MHD effects and keep the fidelity of the formulation by incorporating the numerical method based on the Riccati transformation when quantifying the inner-layer Δ. The proposed scheme reproduces not only the predicted responses in essentially all asymptotic regimes but also with continuous transitions as well as improved accuracies. In particular, the Δ variations across the inertial regimes with viscous or semi-collisional effects have been further resolved, in comparison with additional analytic solutions. The results imply greater shielding of the electromagnetic torque at the layer than what would be expected by earlier work when the viscous or semi-collisional effects can compete against the inertial effects, and also due to the intermediate regulation by kinetic Alfvén wave resonances as rotation slows down. These are important features that can alter the non-axisymmetric plasma responses including the field penetration by external fields or island seeding process in rotating tokamak plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Multichannel spectral estimation in acoustics: A state-space approach

Spectral estimation is a necessary methodology to analyze the frequency content of noisy data sets especially in acoustic applications. Many spectral techniques have evolved starting with the classical Fourier transform methods based on the well-known Wiener-Khintchine relationship relating the covariance-to-spectral density as a transform pair culminating with more elegant model-based parametric techniques that apply prior knowledge of the data to produce a high-resolution spectral estimate. Multichannel spectral representations are a class of both nonparametric, as well as parametric, estimators that provide improved spectral estimates. In any case, classical nonparametric multichannel techniques can provide reasonable estimates when coupled with peak-peaking methods as long as the signal levels are reasonably high. Furthermore, parametric multichannel methods can perform quite well in low signal level environments even when applying simple peak-picking techniques. In this paper, the performance of both nonparametric (periodogram) and parametric (state-space) multichannel spectral estimation methods are investigated when applied to both synthesized noisy structural vibration data as well as data obtained from a sounding rocket flight. It is demonstrated that for the multichannel problem, state-space techniques provide improved performance, offering a parametric alternative compared to classical methods.

42 ENGINEERING↗
NASA NTRS1973

Application of modern control theory to the design of optimum aircraft controllers

A procedure is described for synthesis of optimal aircraft control systems by application of the concepts of optimal control theory to time-invariant linear systems with quadratic performance criteria. Essential in this synthesis procedure is the solution of the Riccati matrix equation which results in a constant linear feedback control law for an output regulator which maintains a plant in an equilibrium in the presence of impulse disturbances. An algorithm is derived for designing maneuverable output regulators with selected state variables for feedback.

Power, L. J.↗
NASA NTRS1980

Linear stochastic optimal control and estimation problem

Problem involves design of controls for linear time-invariant system disturbed by white noise. Solution is Kalman filter coupled through set of optimal regulator gains to produce desired control signal. Key to solution is solving matrix Riccati differential equation. LSOCE effectively solves problem for wide range of practical applications. Program is written in FORTRAN IV for batch execution and has been implemented on IBM 360.

Geyser, L. C.↗
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.↗
NASA NTRS1980

Modal methods in optimal control synthesis

Efficient algorithms for solving linear smoother-follower problems with quadratic criteria are presented. For time-invariant systems, the algorithm consists of one backward integration of a linear vector equation and one forward integration of another linear vector equation. Furthermore, the backward and forward Riccati matrices can be expressed in terms of the eigenvalues and eigenvectors of the Euler-Lagrange equations. Hence, the gains of the forward and backward Kalman-Bucy filters and of the optimal state-feedback regulator can be determined without integration of matrix Riccati equations. A computer program has been developed, based on this method of determining the gains, to synthesize the optimal time-invariant compensator in the presence of random disturbance inputs and random measurement errors. The program also computes the rms state and control variables of the optimal closed-loop system.

Bryson, A. E., Jr.↗
NASA NTRS1990

A homotopy algorithm for synthesizing robust controllers for flexible structures via the maximum entropy design equations

One well known deficiency of LQG compensators is that they do not guarantee any measure of robustness. This deficiency is especially highlighted when considering control design for complex systems such as flexible structures. There has thus been a need to generalize LQG theory to incorporate robustness constraints. Here we describe the maximum entropy approach to robust control design for flexible structures, a generalization of LQG theory, pioneered by Hyland, which has proved useful in practice. The design equations consist of a set of coupled Riccati and Lyapunov equations. A homotopy algorithm that is used to solve these design equations is presented.

Collins, Emmanuel G., Jr.↗
DOE OSTI2024

Leveraging Multitime Hamilton–Jacobi PDEs for Certain Scientific Machine Learning Problems

Hamilton-Jacobi partial differential equations (HJ PDEs) have deep connections with a wide range of fields, including optimal control, differential games, and imaging sciences. By considering the time variable to be a higher dimensional quantity, HJ PDEs can be extended to the multi-time case. In this paper, we establish a novel theoretical connection between specific optimization problems arising in machine learning and the multi-time Hopf formula, which corresponds to a representation of the solution to certain multi-time HJ PDEs. Through this connection, we increase the interpretability of the training process of certain machine learning applications by showing that when we solve these learning problems, we also solve a multi-time HJ PDE and, by extension, its corresponding optimal control problem. As a first exploration of this connection, we develop the relation between the regularized linear regression problem and the Linear Quadratic Regulator (LQR). We then leverage our theoretical connection to adapt standard LQR solvers (namely, those based on the Riccati ordinary differential equations) to design new training approaches for machine learning. Lastly, we provide some numerical examples that demonstrate the versatility and possible computational advantages of our Riccati-based approach in the context of continual learning, post-training calibration, transfer learning, and sparse dynamics identification.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1976

The linear quadratic optimal control problem for infinite dimensional systems over an infinite horizon - Survey and examples

Available published results are surveyed for a special class of infinite-dimensional control systems whose evolution is characterized by a semigroup of operators of class C subscript zero. Emphasis is placed on an approach that clarifies the system-theoretic relationship among controllability, stabilizability, stability, and the existence of a solution to an associated operator equation of the Riccati type. Formulation of the optimal control problem is reviewed along with the asymptotic behavior of solutions to a general system of equations and several theorems concerning L2 stability. Examples are briefly discussed which involve second-order parabolic systems, first-order hyperbolic systems, and distributed boundary control.

Bensoussan, A.↗
NASA NTRS1984

Optimal slewing maneuvers for flexible spacecraft using a closed form solution for the linear tracking problem

The problem of maneuvering a flexible spacecraft through a large angle while requiring the feedback control system to track a desired output state is considered. The desired output state is assumed to be provided by the corresponding open-loop maneuvering solution for the linear system model. Closed form solutions are provided for the Riccati and prefilter equations defining the optimal control. Example maneuvers are presented where control-rate penalties have been included in the performance index, in order to smooth both the open- and closed-loop control commands.

Turner, J. D.↗
NASA NTRS1984

Large-angle maneuvers of flexible spacecraft using a closed form solution for the terminal tracking problem

The problem of maneuvering a flexible spacecraft through a large-angle while requiring a sub-vector of the terminal state to exactly satisfy a set of terminal constraints is considered. The necessary conditions for this problem lead to three coupled nonlinear Riccati-like differential equations, which are solved in closed form. Example maneuvers are presented where control-rate penalties have been included in the performance index, in order to smooth the closed-loop control commands. Furthermore, example maneuvers are presented for both fixed and free and condition problem.

Juan, J.-N.↗
NASA NTRS1986

Toward a systematic design theory for silicon solar cells using optimization techniques

This work is a first detailed attempt to systematize the design of silicon solar cells. Design principles follow from three theorems. Although the results hold only under low injection conditions in base and emitter regions, they hold for arbitrary doping profiles and include the effects of drift fields, high/low junctions and heavy doping concentrations of donor or acceptor atoms. Several optimal designs are derived from the theorems, one of which involves a three-dimensional morphology in the emitter region. The theorems are derived from a nonlinear differential equation of the Riccati form, the dependent variable of which is a normalized recombination particle current.

Misiakos, K.↗
NASA NTRS1989

Integrated control-system design via generalized LQG (GLQG) theory

Thirty years of control systems research has produced an enormous body of theoretical results in feedback synthesis. Yet such results see relatively little practical application, and there remains an unsettling gap between classical single-loop techniques (Nyquist, Bode, root locus, pole placement) and modern multivariable approaches (LQG and H infinity theory). Large scale, complex systems, such as high performance aircraft and flexible space structures, now demand efficient, reliable design of multivariable feedback controllers which optimally tradeoff performance against modeling accuracy, bandwidth, sensor noise, actuator power, and control law complexity. A methodology is described which encompasses numerous practical design constraints within a single unified formulation. The approach, which is based upon coupled systems or modified Riccati and Lyapunov equations, encompasses time-domain linear-quadratic-Gaussian theory and frequency-domain H theory, as well as classical objectives such as gain and phase margin via the Nyquist circle criterion. In addition, this approach encompasses the optimal projection approach to reduced-order controller design. The current status of the overall theory will be reviewed including both continuous-time and discrete-time (sampled-data) formulations.

Bernstein, Dennis S.↗