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At least 163 records · Page 9

All sources NASA NTRS DOE OSTI

DOE OSTI2023

Nearly Periodic Maps and Geometric Integration of Noncanonical Hamiltonian Systems

Abstract M. Kruskal showed that each continuous-time nearly periodic dynamical system admits a formal U (1)-symmetry, generated by the so-called roto-rate. When the nearly periodic system is also Hamiltonian, Noether’s theorem implies the existence of a corresponding adiabatic invariant. We develop a discrete-time analog of Kruskal’s theory. Nearly periodic maps are defined as parameter-dependent diffeomorphisms that limit to rotations along a U (1)-action. When the limiting rotation is non-resonant, these maps admit formal U (1)-symmetries to all orders in perturbation theory. For Hamiltonian nearly periodic maps on exact presymplectic manifolds, we prove that the formal U (1)-symmetry gives rise to a discrete-time adiabatic invariant using a discrete-time extension of Noether’s theorem. When the unperturbed U (1)-orbits are contractible, we also find a discrete-time adiabatic invariant for mappings that are merely presymplectic, rather than Hamiltonian. As an application of the theory, we use it to develop a novel technique for geometric integration of non-canonical Hamiltonian systems on exact symplectic manifolds.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Hybrid model predictive control techniques for safety factor profile and stored energy regulation while incorporating NBI constraints

Abstract A novel hybrid Model Predictive Control (MPC) algorithm has been designed for simultaneous safety factor ( q ) profile and stored energy ( w ) control while incorporating the pulse-width-modulation constraints associated with the neutral beam injection (NBI) system. Regulation of the q -profile has been extensively shown to be a key factor for improved confinement as well as non-inductive sustainment of the plasma current. Simultaneous control of w is necessary to prevent the triggering of pressure-driven magnetohydrodynamic instabilities as the controller shapes the q profile. Conventional MPC schemes proposed for q -profile control have considered the NBI powers as continuous-time signals, ignoring the discrete-time nature of these actuators and leading in some cases to performance loss. The hybrid MPC scheme in this work has the capability of incorporating the discrete-time actuator dynamics as additional constraints. In nonlinear simulations, the proposed hybrid MPC scheme demonstrates improved q -profile+ w control performance for NSTX-U operating scenarios.

Physics↗

NASA NTRS1987

Performance evaluation of fault tolerant systems represented by Markov models

A method to evaluate the performance of fault tolerant systems whose configuration can be represented by time-invariant, discrete-time, discrete-state Markov models is introduced. Each state is assumed to be associated with a constant qualitative measure of the system's performance. The method first computes the moments of the performance probability mass function (PMF) and then finds an approximating function that has the same moments. The form of this function is a maximum entropy solution of the moment matching problem. A simple algorithm for calculating the necessary moments is derived and a method for finding the approximate performance PMF is suggested. After some modification, the method is applied to an example, the Inertial Upper Stage navigation system.

Missana, Jean-Olivier A. A.↗

NASA NTRS2004

Stochastic Stability of Nonlinear Sampled Data Systems with a Jump Linear Controller

This paper analyzes the stability of a sampled- data system consisting of a deterministic, nonlinear, time- invariant, continuous-time plant and a stochastic, discrete- time, jump linear controller. The jump linear controller mod- els, for example, computer systems and communication net- works that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. To analyze stability, appropriate topologies are introduced for the signal spaces of the sampled- data system. With these topologies, the ideal sampling and zero-order-hold operators are shown to be measurable maps. This paper shows that the known equivalence between the stability of a deterministic, linear sampled-data system and its associated discrete-time representation as well as between a nonlinear sampled-data system and a linearized representation holds even in a stochastic framework.

Gonzalez, Oscar R.↗

NASA NTRS1991

Covariance control of discrete stochastic bilinear systems

The covariances that certain bilinear stochastic discrete time systems may possess are characterized. An explicit parameterization of all controllers that assign such covariances is given. The state feedback assignability and robustness of the system are discussed from a deterministic point of view. This work extends the theory of covariance control for continuous time bilinear systems to a discrete time setting.

Skelton, R. E.↗

DOE OSTI2023

Geiger-mode laser vibrometry methods and systems

Systems and methods for Geiger-mode laser vibrometry are described. An example method for laser vibrometry includes receiving a first time-series of single photon arrivals corresponding to a laser beam reflected from or transmitted through a target, the single photon arrivals including information corresponding to vibrations of the target, each single photon arrival separated in time from another single photon arrival, determining, based on two or more of the single photon arrivals, a discrete time sequence having a binary value, and generating a second time-series by assigning a non-binary value to each of the discrete time points, wherein each of the assigned non-binary values is determined based on a number of discrete time points lacking a photon arrival prior to receiving a photon.

Little, Liesl M.↗

NASA NTRS1999

Aerodynamic and Aeroelastic Insights using Eigenanalysis

This paper presents novel analytical results for eigenvalues and eigenvectors produced using discrete time aerodynamic and aeroelastic models. An unsteady, incompressible vortex lattice aerodynamic model is formulated in discrete time; the importance of several modeling parameters is examined. A detailed study is made of the behavior of the aerodynamic eigenvalues both in discrete and continuous time. The aerodynamic model is then incorporated into aeroelastic equations of motion. Eigenanalyses of the coupled equations produce stability results and modal characteristics which are valid for critical and non-critical velocities. Insight into the modeling and physics associated with aeroelastic system behavior is gained by examining both the eigenvalues and the eigenvectors. Potential pitfalls in discrete time model construction and analysis are examined.

Heeg, Jennifer↗

NASA NTRS2004

Aerodynamic and Aeroelastic Insights using Eigenanalysis

Heeg, Jennifer↗

DOE OSTI2024

Floquet Insulators and Lattice Fermions

Floquet insulators are periodically driven quantum systems that can host novel topological phases as a function of the drive parameters. These new phases exhibit features reminiscent of fermion doubling in discrete-time lattice fermion theories. We make this suggestion concrete by mapping the spectrum of a noninteracting (1+1)D Floquet insulator for certain drive parameters onto that of a discrete-time lattice fermion theory with a time-independent Hamiltonian. The resulting Hamiltonian is distinct from the Floquet Hamiltonian that generates stroboscopic dynamics. Finally, it can take the form of a discrete-time Su-Schrieffer-Heeger model with half the number of spatial sites of the original model, or of a (1+1)D Wilson-Dirac theory with one quarter of the spatial sites.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1994

On the Dynamics of Computing a Chemically Relaxed Nonequilibrium Flow

In order to gain insights into the strong dependence of numerical solutions on initial data for finite time steps, a set of nonlinear test problems rich enough to capture the behavior of difference schemes were recently identified and the numerical basins of attraction for these problems were computed using commonly used time discretizations in CFD. Our study revealed a wealth of surprisingly nonlinear behavior of numerical schemes that were not observed before, in particular for the implicit time discretizations that are commonly used in CFD. The goal of this work is to apply these tools to study a practical model from non-equilibrium flowfield relaxation. This type of problem arises in chemically nonequilibrium hypersonic flows such as in a shock tube experiment or an expanding nozzle. Here we consider a reacting mixture of (N2, N) for an inviscid one-dimensional steady model. Preliminary numerical results indicate that, aside from the possibility of spurious numerical solutions being introduced by the time discretizations, limitations on the model for physical or accurate solutions may also play a part in the dynamics observed.

Sweby, P. K.↗

DOE OSTI2023

Approximation of nearly-periodic symplectic maps via structure-preserving neural networks

A continuous-time dynamical system with parameter ε is nearly-periodic if all its trajectories are periodic with nowhere-vanishing angular frequency as ε approaches 0. Nearly-periodic maps are discrete-time analogues of nearly-periodic systems, defined as parameter-dependent diffeomorphisms that limit to rotations along a circle action, and they admit formal U(1) symmetries to all orders when the limiting rotation is non-resonant. For Hamiltonian nearly-periodic maps on exact presymplectic manifolds, the formal U(1) symmetry gives rise to a discrete-time adiabatic invariant. In this paper, we construct a novel structure-preserving neural network to approximate nearly-periodic symplectic maps. This neural network architecture, which we call symplectic gyroceptron, ensures that the resulting surrogate map is nearly-periodic and symplectic, and that it gives rise to a discrete-time adiabatic invariant and a long-time stability. This new structure-preserving neural network provides a promising architecture for surrogate modeling of non-dissipative dynamical systems that automatically steps over short timescales without introducing spurious instabilities.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1973

Digital flight control design using implicit model following.

A design procedure for determining the control gains of a discrete-time ('digital') control system is presented. The method is separable into four distinct steps: (1) the definition of closed-loop response criteria, (2) the choice of a discrete-time model which provides the desired response, (3) the determination of control gains which implicitly force the actual system to follow the desired response, and (4) the reduction of the measurement state by the introduction of an 'observer' (a form of integral-differential compensation). It is shown that a single desired response does not completely define the 'ideal' system. The response criterion generally leaves some parameters of the model unspecified, allowing two courses for improving the model: (1) definition of additional response criteria, or (2) redefinition of the discrete-time model for improved implicit model-following with the actual closed-loop system.

Stengel, R. F.↗

NASA NTRSDate not supplied

Estimation With Range Depended Sensor Model

This paper focuses on the improvement of object detection accuracy taking into account the sensor’s reading degradation as the relative range increases. The approach is based on the assumption that range measurement error depends on the actual range. Specifically, we model the measurement error as a proportional to the actual range term plus a zero-mean, Gaussian distributed, and uncorrelated process. The tracking problem is considered in a mixed continuous-discrete time domain, where the target dynamics is in continuous-time and the measurements are in discrete-time, which is an optimal choice in many tracking and navigation applications. We adopt a commonly used continuous time coordinate-uncoupled white-noise acceleration model for a point object to describe the target motion, and use Extended Kalman Filter (EKF) framework to estimate the target's state and the unknown proportionality coefficient.

Vahram Stepanyan↗

NASA NTRS1991

Hybrid state-space self-tuning control using dual-rate sampling

This paper presents a hybrid state-space self-tuning control scheme using dual-rate sampling for suboptimal digital adaptive control of linear time-invariant continuous-time multivariable stochastic systems with unknown parameters. An equivalent fast-rate discrete-time state-space innovation model (with estimated states) of the continuous-time system is constructed by using the estimated system parameters and Kalman gain. To utilize the existing optimal regional-pole assignment method developed in the continuous-time domain, the constructed fast-rate discrete-time model is converted into an equivalent continuous-time model for the development of a state-feedback optimal control law with pole placement in a specific region. The developed analog optimal control law is then converted into an equivalent pseudo-slow-rate digital control law via the proposed digital redesign technique, which can be realized via slow-rate digital electronics. The proposed method enables the development of a digitally implementable advanced control algorithm for digital adaptive control of continuous-time multivariable stochastic systems which may be unstable and/or have nonminimum phase.

Shieh, Leang S.↗

DOE OSTI2020

Enhance coherence time in intensely driven quantum systems

Not long ago, it was shown that a discrete time crystal can be realized if a quantum system is periodically driven to a non-equilibrium state. Proof-of-concept experiments are reported by two groups using trapped ions and nitrogen-vacancy centers in diamond, respectively. The concept of discrete time crystals vividly demonstrates that the coherence time of a quantum system may be enhanced by driving the system out of equilibrium. In this project, we want to test this novel concept in another canonical quantum system, the quantum Hall system in a two-dimensional electron gas (2DEG). Compared to other systems, quantum Hall magnetism (QHM) in high quality, industry-compatible GaAs/AlGaAs heterostructures allows for detailed and quantitative studies in a particularly simple and clean environment. This detailed knowledge should help achieve longer coherence times in a driven QHM system. This report will detail the results from a recent study on the stability of the quantum Hall skyrmions (QHS) state at a Landau level filling close to ν = 1 by measuring its current-voltage (I-V) breakdown characteristics under radio-frequency (RF) radiations. We observe that the critical current increases visibly when the RF frequency is right at the Larmor frequency of 75As nuclei, where the hyperfine interaction between electron and nuclear spins perturbs the QHS state most significantly. We believe that this observation is consistent with the novel concept that the coherence time of a quantum system may be enhanced by driving the system out of equilibrium.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2009

Numerical Evaluation of the "Dual-Kernel Counter-flow" Matric Convolution Integral that Arises in Discrete/Continuous (D/C) Control Theory

Discrete/Continuous (D/C) control theory is a new generalized theory of discrete-time control that expands the concept of conventional (exact) discrete-time control to create a framework for design and implementation of discretetime control systems that include a continuous-time command function generator so that actuator commands need not be constant between control decisions, but can be more generally defined and implemented as functions that vary with time across sample period. Because the plant/control system construct contains two linear subsystems arranged in tandem, a novel dual-kernel counter-flow convolution integral appears in the formulation. As part of the D/C system design and implementation process, numerical evaluation of that integral over the sample period is required. Three fundamentally different evaluation methods and associated algorithms are derived for the constant-coefficient case. Numerical results are matched against three available examples that have closed-form solutions.

Nixon, Douglas D.↗

NASA NTRS1988

Multirate digital control system design

Methods for multirate digital control system design are discussed. A simple method for sampling rate selection based on control bandwidths is proposed. Methods for generating a discrete-time state model of a sampled-data plant and a discrete-time equivalent to an analog cost function for a sampled-data plant are described. The succesive loop closures and linear quadratic Gaussian synthesis methods are reviewed, and a constrained optimization synthesis method is introduced. The proposed sampling rate selection, discretization, and synthesis methods are applied to two example design problems. Multirate and single-rate compensators synthesized by the different methods are compared, based on closed-loop responses, with compensators having the same real-time computation load.

Berg, Martin C.↗

DOE OSTI2021

Nondispersing Wave Packets in Lattice Floquet Systems

We show that in a one-dimensional translationally invariant tight binding chain, nondispersing wave packets can in general be realized as Floquet eigenstates—or linear combinations thereof—using a spatially inhomogeneous drive, which can be as simple as modulation on a single site. The recurrence time of these wave packets (their “round-trip” time) locks in at rational ratios sT/r of the driving period T, where s, r are coprime integers. Wave packets of different s / r can coexist under the same drive, yet travel at different speeds. They retain their spatial compactness either infinitely (s/r = 1) or over a long time (s/r ≠ 1). Discrete time translation symmetry is manifestly broken for s ≠ 1, reminiscent of integer and fractional Floquet time crystals. We further demonstrate how to reverse engineer a drive protocol to reproduce a target Floquet micromotion, such as the free propagation of a wave packet, as if coming from a strictly linear energy spectrum. The variety of control schemes open up a new avenue for Floquet engineering in quantum information sciences.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗