Optimal extremal systems
Optimal extremal control system with mean square error of tracking extremum with random inputs, and application to automatic control system
OPTIMAL CONTROL↗
SEARCH · Engineering Papers
Results for “Random Systems”
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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Statistics of internal stress fluctuations in dislocated crystals and relevance to density-based dislocation dynamics models
A statistical analysis of internal stress fluctuations, defined as the difference between the local mean stress and stress on dislocations, is presented for deforming crystals with 3D discrete dislocation systems. Dislocation realizations are generated using dislocation dynamics simulations and the associated stress field is computed as a superposition of a regularized stress field of dislocation lines within the domain of the solution and a complementary stress field computed via a finite-element boundary value problem. The internal stress fluctuations of interest are defined by an ensemble of the difference between the stress on dislocation lines and the local mean field stress in the crystal. The latter is established in a piecewise fashion over small voxels in the crystal thus allowing the difference between the local average stress and stress on segments to be easily estimated. The results show that the Schmid stress (resolved shear stress) and Escaig stress fluctuations on various slip systems sampled over a random set of points follow a Cauchy (Lorentz) distribution at all strain levels, with the amplitude and width of the distribution being dependent on the strain. Finally, the implications of the Schmid and Escaig internal stress fluctuations are discussed from the points of view of dislocation cross-slip and the dislocation motion in continuum dislocation dynamics.
36 MATERIALS SCIENCE↗
Chaotic roots of the modular multiplication dynamical system in Shor's algorithm
Shor's factoring algorithm, believed to provide an exponential speedup over classical computation, relies on finding the period of an exactly periodic quantum modular multiplication operator. This exact periodicity is the hallmark of an integrable system, which is paradoxical from the viewpoint of quantum chaos, given that the classical limit of the modular multiplication operator is a highly chaotic system that occupies the “maximally random” Bernoulli level of the classical ergodic hierarchy. In this work, we approach this apparent paradox from a quantum dynamical systems viewpoint, and consider whether signatures of ergodicity and chaos may indeed be encoded in such an “integrable” quantization of a chaotic system. We show that Shor's modular multiplication operator, in specific cases, can be written as a superposition of quantized 𝐴-baker's maps exhibiting more typical signatures of quantum chaos and ergodicity. This work suggests that the integrability of Shor's modular multiplication operator may stem from the interference of other “chaotic” quantizations of the same family of maps, and paves the way for deeper studies on the interplay of integrability, ergodicity, and chaos in and via quantum algorithms.
Dynamical systems↗
Machine Learning-Assisted Stability Boundary Determination of Multiport Autonomous Reconfigurable Solar Power Plants
The multiport autonomous reconfigurable solar (MARS) power plant is a promising solution to integrate renewable resources and energy storage systems into the alternating current (ac) power grid and an high-voltage direct current (HVdc) link. In the MARS system, various input power sources are connected to the individual submodules (SMs) through direct current (dc)–dc converters. However, the presence of external power sources can result in unbalanced capacitor voltages of SMs, thereby violating stability constraints under multiple/diverse operating conditions. This article aims to address the gap by accurately determining the stability boundary of the MARS system. As such, a novel machine learning (ML)-assisted energy balancing control (EBC) criterion is proposed. Further, in conjunction with a refined EBC, this approach ensures balanced capacitor voltages across various types of SMs, significantly enhancing the overall system efficiency. The proposed EBC criterion effectively controls EBC activation and deactivation, achieving remarkable accuracy. Both power systems computer aided design (PSCAD)/electromagnetic transients including direct current (EMTDC) simulations and control hardware-in-the-loop (cHIL) tests are conducted to validate the feasibility and efficiency of the proposed method. By combining the EBC and ML-assisted EBC criterion, efficient energy management is achieved for systems featuring multiple input power sources, such as MARS. This approach enables the system to fully exploit its potential across an expanded operational range while upholding high-efficiency standards.
14 SOLAR ENERGY↗
Provably efficient machine learning for quantum many-body problems
Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over traditional methods have not been firmly established. In this work, we prove that classical ML algorithms can efficiently predict ground-state properties of gapped Hamiltonians after learning from other Hamiltonians in the same quantum phase of matter. By contrast, under a widely accepted conjecture, classical algorithms that do not learn from data cannot achieve the same guarantee. We also prove that classical ML algorithms can efficiently classify a wide range of quantum phases. Extensive numerical experiments corroborate our theoretical results in a variety of scenarios, including Rydberg atom systems, two-dimensional random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases.
Science & Technology - Other Topics↗
A Machine Learns to Predict the Stability of Highly Diverse Multi-planetary Systems
Machine learning has proven to be an invaluable tool for characterizing the stability of planets in simplified planetary systems. In this work, we investigate the performance of a machine learning classifier on tightlypacked systems containing a rich diversity of planets, from Earths to Jupiters. Using information derived from short numerical simulations about a planet’s early orbital evolution and its relationship with the most massive planets in the system, we train a random forest classifier to predict instability with a > 88 percent accuracy. Our classifier relies on relative planet masses and the standard deviation of eccentricity for much of its predictive power. Most misclassified planets lie along a multi-dimensional boundary between stable and unstable planets, indicating that their early orbital evolution is ambiguous. The major reason for misclassification in this work is timescale: because our classifier uses information from only the first 137 years of simulation data, it is blind to late time interactions that cause or prevent instability. Machine learning methods like those utilized in this work provide powerful tools to complement numerical simulations across a wide range of planetary architectures.
79 ASTRONOMY AND ASTROPHYSICS↗
Representing Complex Systems as Graphs for Debugging and Predictive Maintenance-Preliminary Thoughts
Representing complex systems as graphs enables use of mathematical tools to identify faults or predict failures. Graph nodes correspond to individual modules or subsystems, and edges link coupled system parts. ‘Probes’ measure the node outputs, monitoring the system health for unexpected behavior. Assuming one cannot probe every point, within a system, the fault correlates to a region—not necessarily the specific location. Bayesian networks trained to understand fault patterns can accurately identify the source. The diagnostic tool described aides debugging by pinpointing system failure causes. For predictive maintenance, probe data develop probability distribution functions describing subsystem mean time to failure. Unit lifetime can be estimated through these probability distributions. Two approaches include using Bayesian classifiers to infer the system failure source and developing maintenance schedules by treating systems as collections of random variables. When failure behavior does not follow a closed form function, use of similarity models is proposed.
97 MATHEMATICS AND COMPUTING↗
Deployable Element Ultra-High Vacuum Pump
Advancing Ultra High Vacuum (UHV) Pumping Technology: The deployable UHV pump team has designed a theoretical model to boost efficiency in high vacuum environments. Traditional systems face challenges with random molecular motion. The innovative windmill design, using titanium sublimation technology, reduces randomness by deploying a gettering surface that actively captures particles. This marks a notable advancement in UHV pumping technology.
43 PARTICLE ACCELERATORS↗
Stochastic gradient descent algorithm for stochastic optimization in solving analytic continuation problems
We propose a stochastic gradient descent based optimization algorithm to solve the analytic continuation problem in which we extract real frequency spectra from imaginary time Quantum Monte Carlo data. The procedure of analytic continuation is an ill-posed inverse problem which is usually solved by regularized optimization methods, such like the Maximum Entropy method, or stochastic optimization methods. The main contribution of this work is to improve the performance of stochastic optimization approaches by introducing a supervised stochastic gradient descent algorithm to solve a flipped inverse system which processes the random solutions obtained by a type of Fast and Efficient Stochastic Optimization Method.
97 MATHEMATICS AND COMPUTING↗
Mind the crosscap: $τ$-scaling in non-orientable gravity and time-reversal-invariant systems
Spectral statistics of quantum chaotic systems are governed by random matrix universality. In many cases of interest, time-reversal symmetry selects the Gaussian Orthogonal Ensemble (GOE) as the relevant universality class. In holographic CFTs, this is mirrored by the presence of non-orientable geometries in the dual gravitational path integral. In this work, we analyze general properties of these matrix models and their gravitational counterparts. First, we develop a formalism to express the universal level statistics in the canonical ensemble for arbitrary spectral curves, leading to a topological expansion with finite radius of convergence in the late-time $τ$-scaling limit. Then, we focus on topological gravity and study topological recursion on the moduli space of non-orientable surfaces. We find that the Weil-Petersson volumes display non-analytic behaviour multiplying polynomials in the boundary lengths. The volumes give rise to wormholes with late-time divergences, in contrast with the orientable case, which is finite. We identify systematic cancellations among WP volumes implied by the consistency and finiteness of the $τ$-scaling limit. In particular, the cancellation of late-time divergences requires a nontrivial genus resummation. Working in the gravitational microcanonical ensemble, we derive and resum all orders of the topological expansion matching the GOE matrix model in the high-energy regime.
Chaotic Dynamics (nlin.CD)↗
On system measurement and identification.
System measurement and identification, considering stochastic transformation between input and output functions, noting connection with radio communication problems
RADIO COMMUNICATION↗
Coding System Design for Advanced Solar Missions Final Report
Random tree code review, horseback analysis of concatenation schemes, and simulations in sequential coding system design for advanced solar missions
Source record↗
A conversational language for the computer- controlled vibration laboratory
User-oriented conversational language computer program for Jet Propulsion Laboratory digital control random excitation environmental test system for spacecraft
Chapman, C. P.↗
Concepts for a theoretical and experimental study of lifting rotor random loads and vibrations (the effects of some rotor feedback systems on rotor-body dynamics), Phase 7-A
The effects of three gyroless rotor feedback systems: (1) coning feedback, (2) proportional tilting feedback, and (3) a combination of these on the rotor-body dynamics of hingeless rotorcraft are studied with a simplified analytical model in the advance ratio range from 0 to .8. Combinations of feedback phase angles and control phase angles are selected to minimize control cross coupling and control sensitivity changes between low and high speed flight. For the feedback systems thus selected the effects of feedback gain and control actuator time lag on the stability both with fixed hub and in free flight is studied, whereby the rotorcraft is free in pitch, roll and vertical motion but otherwise restrained. For the free flight is studied, whereby the rotorcraft is free in pitch, roll and vertical motion but otherwise restrained. For the free flight conditions the effects of a horizontal tail are also determined in itself and in combination with the rotor feedback systems.
Hohenemser, K. H.↗
Laser Doppler systems in atmospheric turbulence
The loss of heterodyne signal power for the Marshall Space Flight Center laser Doppler system due to the random changes in the atmospheric index of refraction is investigated. The current status in the physics of low energy laser propagation through turbulent atmosphere is presented. The analysis and approximate evaluation of the loss of the heterodyne signal power due to the atmospheric absorption, scattering, and turbulence are estimated for the conditions of the January 1973 flight tests. Theoretical and experimental signal to noise values are compared. Maximum and minimum values of the atmospheric attenuation over a two way path of 20 km range are calculated as a function of altitude using models of atmosphere, aerosol concentration, and turbulence.
Murty, S. S. R.↗
Control logic to track the outputs of a command generator or randomly forced target
A procedure is presented for synthesizing time-invariant control logic to cause the outputs of a linear plant to track the outputs of an unforced (or randomly forced) linear dynamic system. The control logic uses feed-forward of the reference system state variables and feedback of the plant state variables. The feed-forward gains are obtained from the solution of a linear algebraic matrix equation of the Liapunov type. The feedback gains are the usual regulator gains, determined to stabilize (or augment the stability of) the plant, possibly including integral control. The method is applied here to the design of control logic for a second-order servomechanism to follow a linearly increasing (ramp) signal, an unstable third-order system with two controls to track two separate ramp signals, and a sixth-order system with two controls to track a constant signal and an exponentially decreasing signal (aircraft landing-flare or glide-slope-capture with constant velocity).
Trankle, T. L.↗
Relationships between digital signal processing and control and estimation theory
Research areas associated with digital signal processing and control and estimation theory are identified. Particular attention is given to image processing, system identification problems (parameter identification, linear prediction, least squares, Kalman filtering), stability analyses (the use of the Liapunov theory, frequency domain criteria, passivity), and multiparameter systems, distributed processes, and random fields.
Willsky, A. S.↗
A model of asynchronous iterative algorithms for solving large, sparse, linear systems
Solving large, sparse, linear systems of equations is one of the fundamental problems in large scale scientific and engineering computation. A model of a general class of asynchronous, iterative solution methods for linear systems is developed. In the model, the system is solved by creating several cooperating tasks that each compute a portion of the solution vector. This model is then analyzed to determine the expected intertask data transfer and task computational complexity as functions of the number of tasks. Based on the analysis, recommendations for task partitioning are made. These recommendations are a function of the sparseness of the linear system, its structure (i.e., randomly sparse or banded), and dimension.
Reed, D. A.↗