Generalized recurrence in dynamical systems.
Generalized recurrence in dynamical systems with aid of continuous real valued function on phase space
PHASE-SPACE INTEGRAL↗
SEARCH · Engineering Papers
Results for “dynamic system”
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.
Predictability of weather and climate in a coupled ocean-atmosphere model: A dynamical systems approach
A dynamical systems approach is used to quantify the instantaneous and time-averaged predictability of a low-order moist general circulation model. Specifically, the effects on predictability of incorporating an active ocean circulation, implementing annual solar forcing, and asynchronously coupling the ocean and atmosphere are evaluated. The predictability and structure of the model attractors is compared using the Lyapunov exponents, the local divergence rates, and the correlation, fractal, and Lyapunov dimensions. The Lyapunov exponents measure the average rate of growth of small perturbations on an attractor, while the local divergence rates quantify phase-spatial variations of predictability. These local rates are exploited to efficiently identify and distinguish subtle differences in predictability among attractors. In addition, the predictability of monthly averaged and yearly averaged states is investigated by using attractor reconstruction techniques.
Nese, Jon M.↗
Projective embedding of dynamical systems: Uniform mean field equations
Herein we study embeddings of continuous dynamical systems in larger dimensions via projector operators. We call this technique PEDS, projective embedding of dynamical systems, as the stable fixed point of the original system dynamics are recovered via projection from the higher dimensional space. In this paper we provide a general definition and prove that for a particular type of rank-1 projector operator, the uniform mean field projector, the equations of motion become a mean field approximation of the dynamical system. While in general the embedding depends on a specified variable ordering, the same is not true for the uniform mean field projector. We prove a variety of results on the relationship between the spectrum of the Jacobian for fixed points in the original and in the embedded system. Direct applications of PEDS can be non-convex optimization and machine learning.
97 MATHEMATICS AND COMPUTING↗
Application of the GRC Stirling Convertor System Dynamic Model
The GRC Stirling Convertor System Dynamic Model (SDM) has been developed to simulate dynamic performance of power systems incorporating free-piston Stirling convertors. This paper discusses its use in evaluating system dynamics and other systems concerns. Detailed examples are provided showing the use of the model in evaluation of off-nominal operating conditions. The many degrees of freedom in both the mechanical and electrical domains inherent in the Stirling convertor and the nonlinear dynamics make simulation an attractive analysis tool in conjunction with classical analysis. Application of SDM in studying the relationship of the size of the resonant circuit quality factor (commonly referred to as Q) in the various resonant mechanical and electrical sub-systems is discussed.
Regan, Timothy F.↗
Control and stabilization of nonholonomic dynamic systems
The paper establishes a theoretical framework for the control of nonholonomic dynamic systems, i.e., dynamic systems with nonintegrable constraints, with emphasis on control properties for nonholonomic systems that have no counterpart in holonomic systems. A model for nonholonomic dynamic systems is presented in terms of differential-algebraic equations defined on a phase space. A reduction procedure is carried out to obtain reduced-order state equations. Conditions for smooth asymptotic stabilization to an m-dimensional equilibrium manifold are presented. It is also demonstrated that a single equilibrium solution cannot be asymptotically stabilized using continuous state feedback. An approach using geometric phases is developed as a basis for the control of Caplygin systems.
Bloch, Anthony M.↗
Non-scalar uncertainty: Uncertainty in dynamic systems
The following point is stated throughout the paper: dynamic systems are usually subject to uncertainty, be it the unavoidable quantic uncertainty when working with sufficiently small scales or when working in large scales uncertainty can be allowed by the researcher in order to simplify the problem, or it can be introduced by nonlinear interactions. Even though non-quantic uncertainty can generally be dealt with by using the ordinary probability formalisms, it can also be studied with the proposed non-scalar formalism. Thus, non-scalar uncertainty is a more general theoretical framework giving insight into the nature of uncertainty and providing a practical tool in those cases in which scalar uncertainty is not enough, such as when studying highly nonlinear dynamic systems. This paper's specific contribution is the general concept of non-scalar uncertainty and a first proposal for a methodology. Applications should be based upon this methodology. The advantage of this approach is to provide simpler mathematical models for prediction of the system states. Present conventional tools for dealing with uncertainty prove insufficient for an effective description of some dynamic systems. The main limitations are overcome abandoning ordinary scalar algebra in the real interval (0, 1) in favor of a tensor field with a much richer structure and generality. This approach gives insight into the interpretation of Quantum Mechanics and will have its most profound consequences in the fields of elementary particle physics and nonlinear dynamic systems. Concepts like 'interfering alternatives' and 'discrete states' have an elegant explanation in this framework in terms of properties of dynamic systems such as strange attractors and chaos. The tensor formalism proves especially useful to describe the mechanics of representing dynamic systems with models that are closer to reality and have relatively much simpler solutions. It was found to be wise to get an approximate solution to an accurate model than to get a precise solution to a model constrained by simplifying assumptions. Precision has a very heavy cost in present physical models, but this formalism allows the trade between uncertainty and simplicity. It was found that modeling reality sometimes requires that state transition probabilities should be manipulated as nonscalar quantities, finding at the end that there is always a transformation to get back to scalar probability.
Martinez, Salvador Gutierrez↗
Overview of the GRC Stirling Convertor System Dynamic Model
A Stirling Convertor System Dynamic Model has been developed at the Glenn Research Center for controls, dynamics, and systems development of free-piston convertor power systems. It models the Stirling cycle thermodynamics, heat flow, gas, mechanical, and mounting dynamics, the linear alternator, and the controller. The model's scope extends from the thermal energy input to thermal, mechanical dynamics, and electrical energy out, allowing one to study complex system interactions among subsystems. The model is a non-linear time-domain model containing sub-cycle dynamics, allowing it to simulate transient and dynamic phenomena that other models cannot. The model details and capability are discussed.
Lewandowski, Edward J.↗
Structural inference of networked dynamical systems with universal differential equations
Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical) units to exhibit a wide range of nontrivial behaviors, such as the emergence of coherent structures (e.g., waves and patterns) or otherwise notable dynamics (e.g., synchrony and chaos). Here, we seek to infer (i) the intrinsic physics of a base unit of a population, (ii) the underlying graphical structure shared between units, and (iii) the coupling physics of a given networked dynamical system given observations of nodal states. These tasks are formulated around the notion of the Universal Differential Equation, whereby unknown dynamical systems can be approximated with neural networks, mathematical terms known a priori (albeit with unknown parameterizations), or combinations of the two. We demonstrate the value of these inference tasks by investigating not only future state predictions but also the inference of system behavior on varied network topologies. The effectiveness and utility of these methods are shown with their application to canonical networked nonlinear coupled oscillators.
97 MATHEMATICS AND COMPUTING↗
Similarity Metrics for Closed Loop Dynamic Systems
To what extent and in what ways can two closed-loop dynamic systems be said to be "similar?" This question arises in a wide range of dynamic systems modeling and control system design applications. For example, bounds on error models are fundamental to the controller optimization with modern control design methods. Metrics such as the structured singular value are direct measures of the degree to which properties such as stability or performance are maintained in the presence of specified uncertainties or variations in the plant model. Similarly, controls-related areas such as system identification, model reduction, and experimental model validation employ measures of similarity between multiple realizations of a dynamic system. Each area has its tools and approaches, with each tool more or less suited for one application or the other. Similarity in the context of closed-loop model validation via flight test is subtly different from error measures in the typical controls oriented application. Whereas similarity in a robust control context relates to plant variation and the attendant affect on stability and performance, in this context similarity metrics are sought that assess the relevance of a dynamic system test for the purpose of validating the stability and performance of a "similar" dynamic system. Similarity in the context of system identification is much more relevant than are robust control analogies in that errors between one dynamic system (the test article) and another (the nominal "design" model) are sought for the purpose of bounding the validity of a model for control design and analysis. Yet system identification typically involves open-loop plant models which are independent of the control system (with the exception of limited developments in closed-loop system identification which is nonetheless focused on obtaining open-loop plant models from closed-loop data). Moreover the objectives of system identification are not the same as a flight test and hence system identification error metrics are not directly relevant. In applications such as launch vehicles where the open loop plant is unstable it is similarity of the closed-loop system dynamics of a flight test that are relevant.
Whorton, Mark S.↗
Semi-supervised Learning of Dynamical Systems with Neural Ordinary Differential Equations: A Teacher-Student Model Approach
Modeling dynamical systems is crucial for a wide range of tasks, but it remains challenging due to complex nonlinear dynamics, limited observations, or lack of prior knowledge. Recently, data-driven approaches such as Neural Ordinary Differential Equations (NODE) have shown promising results by leveraging the expressive power of neural networks to model unknown dynamics. However, these approaches often suffer from limited labeled training data, leading to poor generalization and suboptimal predictions. On the other hand, semi-supervised algorithms can utilize abundant unlabeled data and have demonstrated good performance in classification and regression tasks. We propose TS-NODE, the first semi-supervised approach to modeling dynamical systems with NODE. TS-NODE explores cheaply generated synthetic pseudo rollouts to broaden exploration in the state space and to tackle the challenges brought by lack of ground-truth system data under a teacher-student model. TS-NODE employs an unified optimization framework that corrects the teacher model based on the student's feedback while mitigating the potential false system dynamics present in pseudo rollouts. TS-NODE demonstrates significant performance improvements over a baseline Neural ODE model on multiple dynamical system modeling tasks.
Wang, Yu↗
Online data-driven changepoint detection for high-dimensional dynamical systems
In this study, the detection of anomalies or transitions in complex dynamical systems is of critical importance to various applications. In this study, we propose the use of machine learning to detect changepoints for high-dimensional dynamical systems. Here, changepoints indicate instances in time when the underlying dynamical system has a fundamentally different characteristic—which may be due to a change in the model parameters or due to intermittent phenomena arising from the same model. We propose two complementary approaches to achieve this, with the first devised using arguments from probabilistic unsupervised learning and the latter devised using supervised deep learning. To accelerate the deployment of transition detection algorithms in high-dimensional dynamical systems, we introduce dimensionality reduction techniques. Our experiments demonstrate that transitions can be detected efficiently, in real-time, for the two-dimensional forced Kolmogorov flow and the Rössler dynamical system, which are characterized by anomalous regimes in phase space where dynamics are perturbed off the attractor at potentially uneven intervals. Finally, we also demonstrate how variations in the frequency of detected changepoints may be utilized to detect a significant modification to the underlying model parameters by utilizing the Lorenz-63 dynamical system.
97 MATHEMATICS AND COMPUTING↗
Solar dynamic systems
The development of the solar dynamic system is discussed. The benefits of the solar dynamic system over pv systems are enumerated. The history of the solar dynamic development is recounted. The purpose and approach of the advanced development are outlined. Critical concentrator technology and critical heat recover technology are examined.
Dustin, M. O.↗
DYSCO: A software system for modeling general dynamic systems
The DYSCO program has been under development since 1979. It has been funded by Army and Air Force laboratories and by the Kaman Aerospace Corporation. It is presently available at a number of government and nongovernment installations. It has been used to analyze a very broad range of dynamics problems. A principle feature of the software design of DYSCO is the separation of the executive from the technology. The executive, which controls all the operations, is intelligent in the sense that it knows that its function is to assemble differential equations and to prepare them for solution. The technology library contains FORTRAN routines which perform standard functions, such as, computing the equation coefficients of an element (or component) given the local state at any time. The technology library also contains algorithms and procedures for solving the coupled system equations. The system was designed to allow easy additional of technology to the library. Any linear or nonlinear structural entity, control system, or set of ordinary differential equations may be simply coded and added to the library, as well as algorithms for time or frequency domain solution. The program is described with emphasis on its usefulness in easily modeling unusual concepts and configurations, performing analysis of damage, evaluating new algorithms, and simulating dynamic tests.
Berman, Alex↗
On ''A method for simplifying linear dynamic systems.''
Equation for linear dynamic systems simplification applicable to all cases irrespective of nature of eigenvalues and eigenvectors
EIGENVALUE↗
Identification of dynamic systems, theory and formulation
The problem of estimating parameters of dynamic systems is addressed in order to present the theoretical basis of system identification and parameter estimation in a manner that is complete and rigorous, yet understandable with minimal prerequisites. Maximum likelihood and related estimators are highlighted. The approach used requires familiarity with calculus, linear algebra, and probability, but does not require knowledge of stochastic processes or functional analysis. The treatment emphasizes unification of the various areas in estimation in dynamic systems is treated as a direct outgrowth of the static system theory. Topics covered include basic concepts and definitions; numerical optimization methods; probability; statistical estimators; estimation in static systems; stochastic processes; state estimation in dynamic systems; output error, filter error, and equation error methods of parameter estimation in dynamic systems, and the accuracy of the estimates.
Maine, R. E.↗
An Evaluation of the Applicability of Damage Tolerance to Dynamic Systems
The Federal Aviation Administration, the National Aeronautics and Space Administration and the aircraft industry have teamed together to develop methods and guidance for the safe life-cycle management of dynamic systems. Based on the success of the United States Air Force damage tolerance initiative for airframe structure, a crack growth based damage tolerance approach is being examined for implementation into the design and management of dynamic systems. However, dynamic systems accumulate millions of vibratory cycles per flight hour, more than 12,000 times faster than an airframe system. If a detectable crack develops in a dynamic system, the time to failure is extremely short, less than 100 flight hours in most cases, leaving little room for error in the material characterization, life cycle analysis, nondestructive inspection and maintenance processes. In this paper, the authors review the damage tolerant design process focusing on uncertainties that affect dynamic systems and evaluate the applicability of damage tolerance on dynamic systems.
Forth, Scott C.↗
What is (quantitative) system dynamics modeling? Defining characteristics and the opportunities they create
A clear definition of system dynamics modeling can provide shared understanding and clarify the impact of the field. We introduce a set of characteristics that define quantitative system dynamics, selected to capture core philosophy, describe theoretical and practical principles, and apply to historical work but be flexible enough to remain relevant as the field progresses. The defining characteristics are: (1) models are based on causal feedback structure, (2) accumulations and delays are foundational, (3) models are equation-based, (4) concept of time is continuous, and (5) analysis focuses on feedback dynamics. We discuss the implications of these principles and use them to identify research opportunities in which the system dynamics field can advance. These research opportunities include causality, disaggregation, data science and AI, and contributing to scientific advancement. Progress in these areas has the potential to improve both the science and practice of system dynamics.
97 MATHEMATICS AND COMPUTING↗
On optimal control of hybrid dynamical systems using complementarity constraints
Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate them using non-smooth and non-convex complementarity constraints as a mathematical program with complementarity constraints (MPCC). We utilize a moving finite element based strategy to discretize the differential equation system to accurately locate the unknown switching points at the finite element boundary and achieve high-order accuracy at intermediate non-collocation points. We propose a globalization approach to solve the discretized MPCC problem using a mixed NLP/MILP-based strategy to converge to a non-spurious first-order optimal solution. The method is tested on three dynamic optimization examples, including a gas–liquid tank model and an optimal control problem with a sliding mode solution.
97 MATHEMATICS AND COMPUTING↗