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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Analog and symbolic computation through the Koopman framework

We develop a Koopman operator framework for studying the computational structure of dynamical systems. Specifically, we show that the resolvent of the Koopman operator provides a natural abstraction of halting, yielding a ‘Koopman halting problem’ that is recursively enumerable in general. For symbolic systems, such as those defined on Cantor space, this operator formulation captures reachability between clopen sets, while for equicontinuous systems we prove that the Koopman halting problem is decidable. Our framework demonstrates that absorbing (halting) states in coarse-grained finite automata correspond to Koopman eigenfunctions with eigenvalue one, while cycles in the transition graph impose spectral constraints associated with periodic dynamics. These results provide a unifying perspective on computation in symbolic and analog systems, showing how computational universality is reflected in operator spectra, invariant subspaces, and algebraic structures. Beyond symbolic dynamics, this operator-theoretic lens opens pathways to analyze the computational properties of a broader class of dynamical systems, including polynomial and analog models, and suggests that computational hardness may admit dynamical signatures in terms of Koopman spectral structure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1974

An experimental study of a hybrid adaptive control system

A Liapunov type model reference adaptive control system with five adjustable gains is implemented using a PDP-11 digital computer and an EAI 380 analog computer. The plant controlled is a laboratory type dc servo system. It is made to follow closely a second order linear model. The experimental results demonstrate the feasibility of implementing this rather complex design using only a minicomputer and a reasonable number of operational amplifiers. Also, it points out that satisfactory performance can be achieved even when certain assumptions necessary for the theory are not satisfied.

Lizewski, E. F.↗
NASA NTRS1986

Ab initio study of the ground state surface of Cu3

The ground state surface of the metallic trimer Cu3 is investigated theoretically. Relativistic and correlation effects are taken into account in ab initio computations, which are calibrated against analogous computations for the 1Sigma(g)+ state of Cu2; the results are presented in tables and analyzed. The Cu3 ground state is found to have a 2B2 C(2v) structure with angle greater than 60 deg, lying 59/cm below a 2A1 C(2v) geometry and 280/cm below the D(3h) equilateral geometry. These findings are shown to be in good agreement with the experimental measurements of Rohlfing and Valentini (1986) and their analysis (in terms of a Jahn-Teller distortion of 2E-prime equilateral-triangle geometry) by Truhlar et al. (1986).

Langhoff, Stephen R.↗
NASA NTRS1991

An experimental study of nonlinear dynamic system identification

A technique based on the Minimum Model Error optimal estimation approach is employed for robust identification of a nonlinear dynamic system. A simple harmonic oscillator with quadratic position feedback was simulated on an analog computer. With the aid of analog measurements and an assumed linear model, the Minimum Model Error Algorithm accurately identifies the quadratic nonlinearity. The tests demonstrate that the method is robust with respect to prior ignorance of the nonlinear system model and with respect to measurement record length, regardless of initial conditions.

Stry, Greselda I.↗
NASA NTRS1972

Design of a specialized computer for on-line monitoring of cardiac stroke volume

The design of a specialized analog computer for on-line determination of cardiac stroke volume by means of a modified version of the pressure pulse contour method is presented. The design consists of an analog circuit for computation and a timing circuit for detecting necessary events on the pressure waveform. Readouts of arterial pressures, systolic duration, heart rate, percent change in stroke volume, and percent change in cardiac output are provided for monitoring cardiac patients. Laboratory results showed that computational accuracy was within 3 percent, while animal experiments verified the operational capability of the computer. Patient safety considerations are also discussed.

Webb, J. A., Jr.↗
NASA NTRS1975

A hybrid computer time code reader used to digitize sounding rocket data

A technique is described for utilizing a hybrid computer as a time code reader and digitizer. The NASA 36-bit time code is an absolute time reference for digitizing analog signals to 1 mV resolution at a 1 kHz sampling rate. The analog computer circuit and the operation of the merged analog and digital computer systems is described. A result of this digitization process applied to analog signals recorded on magnetic tape during an auroral sounding rocket flight is given as an example. This is a general technique that could be applied to other areas such as geology, meteorology, oceanography, and seismology.

Dukich, T.↗
NASA NTRS2024

Accelerating Continuous Variable Coherent Ising Machines Via Momentum

The Coherent Ising Machine (CIM) is a non-conventional architecture that takes inspiration from physical annealing processes to solve Ising problems heuristically. Its dynamics are naturally continuous and described by a set of ordinary differential equations that have been proven to be useful for the optimization of continuous variables nonconvex quadratic optimization problems. The dynamics of such Continuous Variable CIMs (CV-CIM) encourage optimization via optical pulses whose amplitudes are determined by the negative gradient of the objective; however, standard gradient descent is known to be trapped by local minima and hampered by poor problem conditioning. In this work, we propose to modify the CV-CIM dynamics using more sophisticated pulse injections based on tried-and-true optimization techniques such as momentum and Adam. Through numerical experiments, we show that the momentum and Adam updates can significantly speed up the CV-CIM’s convergence and improve sample diversity over the original CV-CIM dynamics. We also find that the Adam-CV-CIM’s performance is more stable as a function of feedback strength, especially on poorly conditioned instances, resulting in an algorithm that is more robust, reliable, and easily tunable. More broadly, we identify the CIM dynamical framework as a fertile opportunity for exploring the intersection of classical optimization and modern analog computing.

Ising Model↗
NASA NTRS1992

Comparison of optics and electronics for the calculation of matrix-vector products

Optical processors are attractive because of their ability to perform massively parallel operations such as matrix vector products. The inherently analog nature of optical calculations requires that optical processors be based on analog computations. While the speed at which such analog operations can be performed as well as the natural parallelism of optical systems are great advantages of optical processors, the analog representation of values severely limits the achievable accuracy. Furthermore, optical processors are limited by the need to convert information to and from the intensity of light. Digitization can be used to increase the accuracy of optical matrix-vector processors, but causes a severe reduction in speed. This paper compares the throughput and power requirements of optical and electronic processors, showing that optical matrix-vector processors can provide a greater number of operations/Watt than conventional electronics.

Gary, C. K.↗
NASA NTRS1972

Dynamic verification of a digital flight control system.

Development of a digital control system dynamic variation technique which accounts for the limitation of available frequency response analyzers. Digital control system theory is briefly reviewed, and generation of the necessary theoretical frequency responses is discussed. Results of the dynamic verification of a digital control system for a Saturn V launch vehicle are presented, and attention is given to the limitations of this technique along with its applicability to other types of digital control systems. A technique for performing open-loop frequency response analyses of a flight program implemented in a 'flight-type' digital computer and interface hardware with vehicle dynamics simulated on an analog computer is described.

Nabers, J. P., Jr.↗