SEARCH · Search NASA
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
A set of linear homogeneous nonautonomous ordinary differential equations for which a general solution can be written is developed and discussed. The stability and convergence properties of standard finite-difference methods used to integrate these equations are also considered.
We develop a data-driven framework for learning and correcting nonautonomous vehicle dynamics. Physics-based vehicle models are often simplified for tractability and therefore exhibit inherent model-form uncertainty, motivating the need for data-driven correction. Moreover, nonautonomous dynamics are governed by time-dependent control inputs, which pose challenges in learning predictive models directly from temporal snapshot data. To address these, we reformulate the vehicle dynamics via a local parameterization of the time-dependent inputs, yielding a modified system composed ofa sequence of local parametric dynamical systems. Here, we approximate these parametric systems using two complementary approaches. First, we employ the dimension reduction and interpolation in parameter space (DRIPS) methodology to construct efficient linear surrogate models, equipped with lifted observable spaces and manifold-based operator interpolation. This enables data-efficient learning of vehicle models whose dynamics admit accurate linear representations in the lifted spaces. Second, for more strongly nonlinear systems, we employ flow map learning (FML), a deep neural network (DNN) approach that approximates the parametric evolution map without requiring special treatment of nonlinearities. We further extend FML with a transfer-learning-based model correction procedure, enabling the correction of misspecified prior models using only a sparse set of high-fidelity or experimental measurements, without assuming a prescribed form for the correction term. Through a suite of numerical experiments on unicycle, simplified bicycle, and slip-based bicycle models, we demonstrate that DRIPS offers robust and highly data-efficient learning of nonautonomous vehicle dynamics, while FML provides expressive nonlinear modeling and effective correction of model-form errors under severe data scarcity.
A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.
Various design areas of concern in navigation and control of space-based orbital maneuvering systems such as those on the Orbiter are discussed, with note taken of approach maneuvers. Design problems occur in the areas of storage modes, sensing, activation methods, navigation, target/mission determination, rendezvous and docking schemes, reliability, and commonality between low- and high-energy maneuvering vehicles. Navigation may be in autonomous or nonautonomous modes and may include ground-baed computations and commands via the TDRSS or NORAD systems. Autonomous operations would interface with the GPS. All the concepts discussed are significant for the planned orbital transfer and orbital maneuvering vehicles, which would be used to place satellites in orbit and repair or retrieve them.
It is shown how globally stable model reference adaptive control systems may be designed using only the plant's input and output signals. Controllers for single input-single output, nonlinear, nonautonomous plants are developed based on Liapunov's direct method and the Meyer-Kalman-Yacubovich lemma. Filtered derivatives of the plant output replace pure derivatives which are normally required in these systems. An augmented error signal replaces the error previously used which is the difference between the model and plant outputs. However, global stability is assured in the sense that this difference approaches zero asymptotically.
It is assumed that since the solar paddle attachments to the hub of the spacecraft are not rigidly locked, the effect of the solar panels can be replaced by a constant reaction torque acting on the hub of the spacecraft. This could result in the satellite having an equilibrium motion about an axis displaced from the nominal axis of symmetry. The variational equations of motion are developed about such an equilibrium position using the SAS-A spacecraft as a model. Energy dissipation on the rotor as well as the main body is included. This nonautonomous set of differential equations are linearized and transformed to an autonomous set using the Liapunov reducibility theorem. The stability of the kinematically similar system is examined numerically using representative SAS-A parameters for the case when either pair of solar panels is assumed to be loosely attached. Stability is verified for small system nutation angles (0.1 degree).
The nutational stability of a dual-spin satellite under the influence of an applied reaction torque is analyzed. It is assumed that since the solar paddle attachments to the hub of the spacecraft are not rigidly locked, the effect of the solar panels can be replaced by a constant reaction torque acting on the hub of the spacecraft. This could result in the satellite having an equilibrium motion about an axis displaced from the nominal axis of symmetry. The variational equations of motion are developed about such an equilibrium position using the SAS-A spacecraft as a model. Energy dissipation on the rotor as well as the main body is included. This nonautonomous set of differential equations are linearized and transformed to an autonomous set using the Lyapunov Reducibility Theorem. The stability of the kinematically similar system is examined numerically using representative SAS-A parameters for the case when either pair of solar panels is assumed to be loosely attached. Stability is verified for small system nutation angles (0.1 degree) although the time constant associated with the least damped mode is approximately one order of magnitude larger than that for the SAS-A system without the influence of the reaction torques.
It is shown how globally stable model reference adaptive control systems may be designed when one has access to only the plant's input and output signals. Controllers for single input-single output, nonlinear, nonautonomous plants are developed based on Lyapunov's direct method and the Meyer-Kalman-Yacubovich lemma. Derivatives of the plant output are not required, but are replaced by filtered derivative signals. An augmented error signal replaces the error normally used, which is defined as the difference between the model and plant outputs. However, global stability is assured in the sense that the normally used error signal approaches zero asymptotically.
A method for designing discrete model reference adaptive control systems when one has access to only the plant's input and output signals is given. Controllers for single-input, single-output, nonlinear, nonautonomous plants are developed via Liapunov's second method. Anticipative values of the plant output are not required, but are replaced by signals easily obtained from a low-pass filter operating on the plant's output. The augmented error signal method is employed, ensuring finally that the normally used error signal also approaches zero asymptotically.
A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.
A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.
The work presented is motivated by the need for a national satellite rescue policy, not the ad hoc policy now in place. In studying different approaches for a national policy, the issue of capture and stabilization of a tumbling spacecraft must be addressed. For a rescue mission involving a tumbling spacecraft, it may be advantageous to have a rescue vehicle which is compact and 'rigid' during the rendezvous/capture phase. After capture, passive stabilization techniques could be utilized as an efficient means of detumbling the resulting system (i.e., both the rescue vehicle and captures spacecraft). Since the rescue vehicle is initially compact and 'rigid,' significant passive stabilization through energy dissipation can only be achieved through the deployment of flexible appendages. Once stabilization is accomplished, retraction of the appendages before maneuvering the system to its final destination may also prove advantageous. It is therefore of paramount interest that we study the effect of appendage deployment/retraction on the attitude stability of a spacecraft. Particular interest should be paid to appendage retraction, since if this process is destabilizing, passive stabilization as proposed may not be useful. Over the past three decades, it has been an 'on-again-off-again affair' with the problem of spacecraft appendage deployment. In most instances, these studies have been numerical simulations of specific spacecraft configurations for which there were specific concerns. The primary focus of these studies was the behavior of the appendage during deployment; the effects of appendage retraction was considered only in one of these studies. What is missing in the literature is a thorough study of the effects of appendage deployment/retraction on the attitude stability of a spacecraft. This paper presents a rigorous analysis of the stability of a spinning spacecraft during the deployment or the retraction of an appendage. The analysis is simplified such that meaningful insights into the problem can be inferred; it is not overly simplified such that critical dynamical behavior is neglected. The system is analyzed assuming that the spacecraft hub is rigid. The appendage deployment mechanism is modeled as a point mass on a massless rod whose length undergoes prescribed changes. Simplified flexibility effects of the appendage are included. The system is examined for stability by linearizing the equations in terms of small deviations from steady, noninterfering coning motion. Routh's procedure for analyzing small deviations from steady motion in dynamical systems is utilized in the analysis. The system of equations are nondimensionalized to facilitate parametric studies. The results are presented in terms of a reduced number of nondimensional parameters so that some general conclusions may be drawn. Verification of the linear analysis is presented through numerical simulations of the complete nonlinear, nonautonomous, coupled equations.
Several (global) topological properties of various spaces of linear systems, particularly symmetric, lossless, and Hamiltonian systems, and multivariable spectral densities of fixed McMillan degree are announced. The study is motivated by a result asserting that on a connected but not simply connected manifold, it is not possible to find a vector field having a sink as its only critical point. In the scalar case, this is illustrated by showing that only on the space of McMillan degree = /Cauchy index/ = n, scalar transfer functions can one define a globally convergent vector field. This result holds both in discrete-time and for the nonautonomous case. With these motivations in mind, theorems of Bochner and Fogarty are used in showing that spaces of transfer functions defined by symmetry conditions are, in fact, smooth algebraic manifolds.
Free vibrations of a system and vibrations which are multiples of them in frequency are discussed. The corresponding periodic forced vibrations of the type n/m (n is the number of periods of disturbance between periods of movement and m is the number of periods of movement in one period of disturbance), generated by a harmonic or close to harmonic disturbance, are propagated close to the corresponding curves of the free vibrations and their frequency multiples. It has been proposed that investigation of transitional modes of motion and capture regions be carried out by precise methods in phase space, with the least number of coordinates. Thus, for example, for nonautonomous second order equations (for example, the Duffing equations), in place of three variables (coordinates, velocity, phases), it is proposed to use two: velocity during transition of the coordinate through zero and phase.
Digital twins of complex systems must involve a model that is fast, generalizable, and usable for real-time control. For example, high-fidelity nonlinear multiphysics simulations can capture laser-material interactions, but are too slow for optimization or model predictive control (MPC). Reduced-order models, used to accelerate such computation, frequently fail to generalize to unseen inputs or control states. We show theoretically that this failure is intrinsic, i.e., that a learned model is non-unique outside the sampled subspace when its low-rank structure arises from limited excitation and clustered eigenvalues, rather than from a user-imposed truncation alone. Motivated by this result, we propose a control-ready regional surrogate-construction framework for both autonomous and nonautonomous dynamics; it employs Koopman lifting to represent nonlinearities, while preserving spatial locality. We illustrate our approach by constructing a control-ready surrogate for the digital twin of a thermal component of additive-manufacturing process. Our surrogate, localized in space through a von Neumann stencil, is learned from noisy high-fidelity simulations that emulate thermal-camera images collected during the manufacturing. It is linear in thermo-physically augmented states so that MPC reduces to a convex quadratic program. The surrogate requires no online correction, generalizes to unseen scan paths and power profiles of the laser, and is more than three orders of magnitude faster than a finite-difference solver. Furthermore, when the MPC sequence computed on the digital twin is applied to this solver, closed-loop temperature regulation is recovered, showing that the surrogate preserves control-relevant input-output behavior.
OBJECTIVE: To develop a new specific instrument called the Autonomic Symptom Profile to measure autonomic symptoms and test its validity. BACKGROUND: Measuring symptoms is important in the evaluation of quality of life outcomes. There is no validated, self-completed questionnaire on the symptoms of patients with autonomic disorders. METHODS: The questionnaire is 169 items concerning different aspects of autonomic symptoms. The Composite Autonomic Symptom Scale (COMPASS) with item-weighting was established; higher scores indicate more or worse symptoms. Autonomic function tests were performed to generate the Composite Autonomic Scoring Scale (CASS) and to quantify autonomic deficits. We compared the results of the COMPASS with the CASS derived from the Autonomic Reflex Screen to evaluate validity. RESULTS: The instrument was tested in 41 healthy controls (mean age 46.6 years), 33 patients with nonautonomic peripheral neuropathies (mean age 59.5 years), and 39 patients with autonomic failure (mean age 61.1 years). COMPASS scores correlated well with the CASS, demonstrating an acceptable level of content and criterion validity. The mean (+/-SD) overall COMPASS score was 9.8 (+/-9) in controls, 25.9 (+/-17.9) in the patients with nonautonomic peripheral neuropathies, and 52.3 (+/-24.2) in the autonomic failure group. Scores of symptoms of orthostatic intolerance and secretomotor dysfunction best predicted the CASS on multiple stepwise regression analysis. CONCLUSIONS: We describe a questionnaire that measures autonomic symptoms and present evidence for its validity. The instrument shows promise in assessing autonomic symptoms in clinical trials and epidemiologic studies.