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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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Matrix theorem and application to establishing independent coordinates for complex dynamical systems with constraints
Topologies introduced on state space for differential equations to obtain dynamical systems
Neighboring optimal feedback control of multi-input nonlinear dynamic systems
Existence and construction of modified L lag inverses solution method for linear dynamical systems
We consider the class of large-scale dynamical systems consisting of identical subsystems, but with complex connectivity. It is shown that the irreducibility of this large system is directly related to the irreducibility of a simple system, which is obtained by a replacement of the subsystems by integrators.
A sample development scenario using the Flight Dynamics System Software Development Environment (FDS/SDE) is presented. The SDE uses a menu-driven, fill-in-the-blanks format that provides online help at all steps, thus eliminating lengthy training and allowing immediate use of this new software development tool.
A key ingredient in the simulation of self-gravitating astrophysical fluid dynamical systems is the gravitational potential and its gradient. This paper focuses on the development of a mixed method multigrid solver of the Poisson equation formulated so that both the potential and the Cartesian components of its gradient are self-consistently and accurately generated. The method achieves this goal by formulating the problem as a system of four equations for the gravitational potential and the three Cartesian components of the gradient and solves them using a distributed relaxation technique combined with conventional full multigrid V-cycles. The method is described, some tests are presented, and the accuracy of the method is assessed. We also describe how the method has been incorporated into our three-dimensional hydrodynamics code and give an example of an application to the collision of two stars. We end with some remarks about the future developments of the method and some of the applications in which it will be used in astrophysics.
This is the final report for DOE Grant DE-FG02-93ER25164, initiated in 1993. This grant supported research of John Guckenheimer on computational analysis of dynamical systems. During that period, seventeen individuals received PhD degrees under the supervision of Guckenheimer and over fifty publications related to the grant were produced. This document contains copies of these publications.
Existing hypotheses for the dynamical dependence of tropical cyclone genesis and size on latitude depend principally on the Coriolis parameter $f$. These hypotheses are tested via dynamical aquaplanet experiments with uniform thermal forcing in which planetary rotation rate and planetary radius are varied relative to Earth values; the control simulation is also compared to a present-day Earth simulation. Storm genesis rate collapses to a quasi-universal dependence on f that attains its maximum at the critical latitude, where the inverse-$f$ scale and Rhines scale are equal. Minimum genesis distance from the equator is set by the equatorial Rhines (or deformation) scale and not by a minimum value of $f$. Outer storm size qualitatively follows the smaller of the two length scales, including a slow increase with latitude equatorward of 45° in the control simulation, similar to the Earth simulation. The latitude of peak size scales with the critical latitude for varying planetary radius but not rotation rate, possibly because of the dependence of genesis specifically on $f$. The latitudes of peak size and peak packing density scale closely together. Results suggest that temporal effects and interstorm interaction may be significant for size dynamics. More generally, the critical latitude separates two regimes: 1) a mixed wave–cyclone equatorial belt, where wave effects are strong and the Rhines scale likely limits storm size, and 2) a cyclone-filled polar cap, where wave effects are weak and cyclones persist. Finally, the large-planet limit predicts a world nearly covered with long-lived storms, equivalent to the f plane. Overall, spherical geometry is likely important for understanding tropical cyclone genesis and size on Earthlike planets.
Some of the human factor issues involved in effectively combining human and automated systems are examined with particular reference to spaceflights. The concepts of the crew system and crew systems dynamics are defined, and the present status of crew systems is summarized. The possibilities and potential problems aasociated with the use of automated systems are discussed, as are unique capabilities and possible errors introduced by human participants. It is emphasized that the true integration of human and automated systems must allow for the characteristics of both.
This work presents a non-intrusive reduced-order modeling framework for dynamical systems with spatially localized features characterized by slow singular value decay. The proposed approach builds upon two existing methodologies for reduced and full-order non-intrusive modeling, namely Operator Inference (OpInf) and sparse Full-Order Model (sFOM) inference. We decompose the domain into two complementary subdomains that exhibit fast and slow singular value decay. The dynamics of the subdomain exhibiting slow singular value decay are learned with sFOM while the dynamics with intrinsically low dimensionality on the complementary subdomain are learned with OpInf. The resulting, coupled OpInf-sFOM formulation leverages the computational efficiency of OpInf and the high resolution of sFOM, and thus enables fast non-intrusive predictions for conditions beyond those sampled in the training data set. A novel regularization technique with a closed-form solution based on the Gershgorin disk theorem is introduced to promote stable sFOM and OpInf models. We also provide a data-driven indicator for subdomain selection and ensure solution smoothness over the interface via a post-processing interpolation step. We evaluate the efficiency of the approach in terms of offline and online speedup through a quantitative, parametric computational cost analysis. We demonstrate the coupled OpInf-sFOM formulation for two test cases: a one-dimensional Burgers’ model for which accurate predictions beyond the span of the training snapshots are presented, and a two-dimensional parametric model for the Pine Island Glacier ice thickness dynamics, for which the OpInf-sFOM model achieves an average prediction error on the order of 1% with an online speedup factor of approximately 8$\times$ compared to the numerical simulation.
In this work we present a novel technique, based on a trust-region optimization algorithm and second-order trajectory sensitivities, to compute the extreme trajectories of power system dynamic simulations given a bounded set that represents parametric uncertainty. Furthermore, we show how this method, while remaining computationally efficient compared with sampling-based techniques, overcomes the limitations of previous sensitivity-based techniques to approximate the bounds of the trajectories when the local approximation loses validity because of the nonlinearity. We present several numerical experiments that showcase the accuracy and scalability of the technique, including a demonstration on the IEEE New England test system.
In this chapter we explore the potential development of the biofuels industry using the Biomass Scenario Model (BSM), a system dynamics model developed at the National Renewable Energy Laboratory through the support of the U.S. Department of Energy. The BSM is designed to analyze the implications of policy on the development of the supply chain for biofuels in the United States. It explicitly represents the behavior of decision makers such as farmers, investors, fueling station owners, and consumers. We analyze several illustrative case studies that explore a range of policies and discuss how incentives interact with individual parts of the supply chain as well as the industry as a whole. The BSM represents specific incentives that are intended to approximate policy in the form of selected laws and regulations. Through characterizing the decision making behaviors of economic actors within the supply chain that critically influence the adoption rate of new biofuels production technologies and demonstrating synergies among policies, we find that incentives with coordinated impacts on each major element of the supply chain catalyze net effects of decision maker behavior such that the combined incentives are greater than the summed effects of individual incentives in isolation.
Optimization of nonlinear closed-loop dynamic control systems - integral performance function for partial ordering of closed loop controls
Numerical algorithm for determining stability domain of attraction of equilibrium motions of nonlinear dynamical systems - Liapunov functions
In this paper the problem of optimal feedback control of uncertain discrete-time dynamic systems is considered where the uncertain quantities do not have a stochastic description but instead are known to belong to given sets. The problem is converted to a sequential minimax problem and dynamic programming is suggested as a general method for its solution. The notion of a sufficiently informative function, which parallels the notion of a sufficient statistic of stochastic optimal control, is introduced, and conditions under which the optimal controller decomposes into an estimator and an actuator are identified.
In this paper we investigate on the synchronization problem between two different chaotic dynamical system based on the Lyapunov stability theorem by using nonlinear control functions. Active control schemes are used for synchronization Liu system as drive and Rossler system as response. Numerical simulation by using Maple software are used to show effectiveness of the proposed schemes.
Application of generalized exponential smoothing and matrix pseudoinverses to estimation in dynamic systems