Search NASA⌕ Search

SEARCH · Search NASA

Results for “nonlinear dynamical 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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS2009

The Anomalous Low State of LMC X-3

Archival RXTE ASM and PCA observations of the black hole binary LMC X-3 reveal a dramatic and extended low state lasting from December 8, 2003 until March 18, 2004, unprecedented both in its Low luminosity (Lx(2-10keV)=4.2x 1035 ergs s-1, approximately 4 times fainter than ever before seen from LMC X-3 in its low/hard state, and representing 0.15% of its X-ray luminosity during the high/soft state); and Long duration (approximately equal to 100 days, as compared with 5-20 days for 'normal' low/hard state excursions). During this anomalous low state no significant variability is observed on timescales of days-weeks, and the spectrum is well described by a simple power law with index 1.7 plus or minus 0.2. We examine the variability characteristics of LMC X-3 before and after this event using conventional and topological methods, and show that with the exception of the anomalous low state itself the long-term behavior of the source in topological phase space can be completely described in terms of a well-understood nonlinear dynamics system known as the Duffing oscillator, implying that the accretion disk in LMC X-3 is a driven, dissipative system with two solutions competing for control of its time evolution. This work shows that dynamical information and constraints revealed by topological analysis methods can provide a valuable addition to traditional studies of accretion disk behavior.

Smale, A. P.↗
NASA NTRS2005

Generic Kalman Filter Software

The Generic Kalman Filter (GKF) software provides a standard basis for the development of application-specific Kalman-filter programs. Historically, Kalman filters have been implemented by customized programs that must be written, coded, and debugged anew for each unique application, then tested and tuned with simulated or actual measurement data. Total development times for typical Kalman-filter application programs have ranged from months to weeks. The GKF software can simplify the development process and reduce the development time by eliminating the need to re-create the fundamental implementation of the Kalman filter for each new application. The GKF software is written in the ANSI C programming language. It contains a generic Kalman-filter-development directory that, in turn, contains a code for a generic Kalman filter function; more specifically, it contains a generically designed and generically coded implementation of linear, linearized, and extended Kalman filtering algorithms, including algorithms for state- and covariance-update and -propagation functions. The mathematical theory that underlies the algorithms is well known and has been reported extensively in the open technical literature. Also contained in the directory are a header file that defines generic Kalman-filter data structures and prototype functions and template versions of application-specific subfunction and calling navigation/estimation routine code and headers. Once the user has provided a calling routine and the required application-specific subfunctions, the application-specific Kalman-filter software can be compiled and executed immediately. During execution, the generic Kalman-filter function is called from a higher-level navigation or estimation routine that preprocesses measurement data and post-processes output data. The generic Kalman-filter function uses the aforementioned data structures and five implementation- specific subfunctions, which have been developed by the user on the basis of the aforementioned templates. The GKF software can be used to develop many different types of unfactorized Kalman filters. A developer can choose to implement either a linearized or an extended Kalman filter algorithm, without having to modify the GKF software. Control dynamics can be taken into account or neglected in the filter-dynamics model. Filter programs developed by use of the GKF software can be made to propagate equations of motion for linear or nonlinear dynamical systems that are deterministic or stochastic. In addition, filter programs can be made to operate in user-selectable "covariance analysis" and "propagation-only" modes that are useful in design and development stages.

Lisano, Michael E., II↗
NASA NTRS2013

Detection of Moving Targets Using Soliton Resonance Effect

The objective of this research was to develop a fundamentally new method for detecting hidden moving targets within noisy and cluttered data-streams using a novel "soliton resonance" effect in nonlinear dynamical systems. The technique uses an inhomogeneous Korteweg de Vries (KdV) equation containing moving-target information. Solution of the KdV equation will describe a soliton propagating with the same kinematic characteristics as the target. The approach uses the time-dependent data stream obtained with a sensor in form of the "forcing function," which is incorporated in an inhomogeneous KdV equation. When a hidden moving target (which in many ways resembles a soliton) encounters the natural "probe" soliton solution of the KdV equation, a strong resonance phenomenon results that makes the location and motion of the target apparent. Soliton resonance method will amplify the moving target signal, suppressing the noise. The method will be a very effective tool for locating and identifying diverse, highly dynamic targets with ill-defined characteristics in a noisy environment. The soliton resonance method for the detection of moving targets was developed in one and two dimensions. Computer simulations proved that the method could be used for detection of singe point-like targets moving with constant velocities and accelerations in 1D and along straight lines or curved trajectories in 2D. The method also allows estimation of the kinematic characteristics of moving targets, and reconstruction of target trajectories in 2D. The method could be very effective for target detection in the presence of clutter and for the case of target obscurations.

Kulikov, Igor K.↗
NASA NTRS2014

Bifurcation Analysis Using Rigorous Branch and Bound Methods

For the study of nonlinear dynamic systems, it is important to locate the equilibria and bifurcations occurring within a specified computational domain. This paper proposes a new approach for solving these problems and compares it to the numerical continuation method. The new approach is based upon branch and bound and utilizes rigorous enclosure techniques to yield outer bounding sets of both the equilibrium and local bifurcation manifolds. These sets, which comprise the union of hyper-rectangles, can be made to be as tight as desired. Sufficient conditions for the existence of equilibrium and bifurcation points taking the form of algebraic inequality constraints in the state-parameter space are used to calculate their enclosures directly. The enclosures for the bifurcation sets can be computed independently of the equilibrium manifold, and are guaranteed to contain all solutions within the computational domain. A further advantage of this method is the ability to compute a near-maximally sized hyper-rectangle of high dimension centered at a fixed parameter-state point whose elements are guaranteed to exclude all bifurcation points. This hyper-rectangle, which requires a global description of the bifurcation manifold within the computational domain, cannot be obtained otherwise. A test case, based on the dynamics of a UAV subject to uncertain center of gravity location, is used to illustrate the efficacy of the method by comparing it with numerical continuation and to evaluate its computational complexity.

Smith, Andrew P.↗
NASA NTRS2010

Transforming Mean and Osculating Elements Using Numerical Methods

Mean element propagation of perturbed two body orbits has as its mathematical basis averaging theory of nonlinear dynamical systems. Averaged mean elements define the long-term evolution characteristics of an orbit. Using averaging theory, a near identity transformation can be found that transforms the mean elements back to the osculating elements that contain short period terms in addition to the secular and long period mean elements. The ability to perform the conversion is necessary so that orbit design conducted in mean elements can be converted back into osculating results. In the present work, this near identity transformation is found using the Fast Fourier Transform. An efficient method is found that is capable of recovering the osculating elements to first order

averaging↗
NASA NTRS2019

Input Constrained M-MRAC for Multirotors Operating in an Urban Environment

The paper presents a modified model reference adaptive control (M-MRAC) for multi-input multi-output nonlinear dynamical systems with time varying parametric uncertainties and bounded external disturbances. It uses a prediction model to rapidly generate adaptive estimates of the system's uncertainties with adjustable errors that converge to a small neighborhood of the origin. A sufficient condition is derived to specify the region of attraction in the space of initialization errors, design parameters and external commends. The approach is applied to thrust controlled multi-rotor air vehicles operating in an urban environment. It is shown that the designed controller can provide a good tracking of a given trajectory in the unknown urban wind field, assuming that the maximum thrust generated by the rotors is known. The performance of the algorithms are demonstrated in simulations.

Stepanyan, Vahram↗
NASA NTRS1999

Approximated Stable Inversion for Nonlinear Systems with Nonhyperbolic Internal Dynamics

A technique to achieve output tracking for nonminimum phase nonlinear systems with non- hyperbolic internal dynamics is presented. The present paper integrates stable inversion techniques (that achieve exact-tracking) with approximation techniques (that modify the internal dynamics) to circumvent the nonhyperbolicity of the internal dynamics - this nonhyperbolicity is an obstruction to applying presently available stable inversion techniques. The theory is developed for nonlinear systems and the method is applied to a two-cart with inverted-pendulum example.

Devasia, Santosh↗
NASA NTRS1981

Nonparametric identification of a class of nonlinear close-coupled dynamic systems

A nonparametric identification technique for the identification of close coupled dynamic systems with arbitrary memoryless nonlinearities is presented. The method utilizes noisy recorded data (acceleration, velocity and displacement) to identify the restoring forces in the system. The masses in the system are assumed to be known (or fairly well estimated from the design drawings). The restoring forces are expanded in a series of orthogonal polnomials and the coefficients of these polynomial expansions are obtained by using least square fit method. A particularly simple and computationally efficient method is proposed for dealing with separable restoring forces. The identified results are found to be relatively insensitive to measurement noise. An analysis of the effects of measurement noise on the quality of the estimates is given. The computations are shown to be relatively quick (when compared say to the Wiener identification method) and the core storage required relatively small, making the method suitable for onboard identification of large space structures.

Udwadia, F. E.↗
NASA NTRS1989

Assessment of numerical methods for the solution of fluid dynamics equations for nonlinear resonance systems

The capability of accurate nonlinear flow analysis of resonance systems is essential in many problems, including combustion instability. Classical numerical schemes are either too diffusive or too dispersive especially for transient problems. In the last few years, significant progress has been made in the numerical methods for flows with shocks. The objective was to assess advanced shock capturing schemes on transient flows. Several numerical schemes were tested including TVD, MUSCL, ENO, FCT, and Riemann Solver Godunov type schemes. A systematic assessment was performed on scalar transport, Burgers' and gas dynamic problems. Several shock capturing schemes are compared on fast transient resonant pipe flow problems. A system of 1-D nonlinear hyperbolic gas dynamics equations is solved to predict propagation of finite amplitude waves, the wave steepening, formation, propagation, and reflection of shocks for several hundred wave cycles. It is shown that high accuracy schemes can be used for direct, exact nonlinear analysis of combustion instability problems, preserving high harmonic energy content for long periods of time.

Przekwas, A. J.↗
NASA NTRS1992

Clustering of tethered satellite system simulation data by an adaptive neuro-fuzzy algorithm

Recent developments in neuro-fuzzy systems indicate that the concepts of adaptive pattern recognition, when used to identify appropriate control actions corresponding to clusters of patterns representing system states in dynamic nonlinear control systems, may result in innovative designs. A modular, unsupervised neural network architecture, in which fuzzy learning rules have been embedded is used for on-line identification of similar states. The architecture and control rules involved in Adaptive Fuzzy Leader Clustering (AFLC) allow this system to be incorporated in control systems for identification of system states corresponding to specific control actions. We have used this algorithm to cluster the simulation data of Tethered Satellite System (TSS) to estimate the range of delta voltages necessary to maintain the desired length rate of the tether. The AFLC algorithm is capable of on-line estimation of the appropriate control voltages from the corresponding length error and length rate error without a priori knowledge of their membership functions and familarity with the behavior of the Tethered Satellite System.

Mitra, Sunanda↗
NASA NTRS2004

Learning to Control Advanced Life Support Systems

Advanced life support systems have many interacting processes and limited resources. Controlling and optimizing advanced life support systems presents unique challenges. In particular, advanced life support systems are nonlinear coupled dynamical systems and it is difficult for humans to take all interactions into account to design an effective control strategy. In this project. we developed several reinforcement learning controllers that actively explore the space of possible control strategies, guided by rewards from a user specified long term objective function. We evaluated these controllers using a discrete event simulation of an advanced life support system. This simulation, called BioSim, designed by Nasa scientists David Kortenkamp and Scott Bell has multiple, interacting life support modules including crew, food production, air revitalization, water recovery, solid waste incineration and power. They are implemented in a consumer/producer relationship in which certain modules produce resources that are consumed by other modules. Stores hold resources between modules. Control of this simulation is via adjusting flows of resources between modules and into/out of stores. We developed adaptive algorithms that control the flow of resources in BioSim. Our learning algorithms discovered several ingenious strategies for maximizing mission length by controlling the air and water recycling systems as well as crop planting schedules. By exploiting non-linearities in the overall system dynamics, the learned controllers easily out- performed controllers written by human experts. In sum, we accomplished three goals. We (1) developed foundations for learning models of coupled dynamical systems by active exploration of the state space, (2) developed and tested algorithms that learn to efficiently control air and water recycling processes as well as crop scheduling in Biosim, and (3) developed an understanding of the role machine learning in designing control systems for advanced life support.

Subramanian, Devika↗
NASA NTRS2018

Modeling and Control Design for a Turboelectric Single Aisle Aircraft Propulsion System

A nonlinear dynamic model with full flight envelope controller is developed for the propulsion system of a partially turboelectric single-aisle aircraft. The propulsion system model consists of two turbofan engines with a large percentage of power extraction, feeding an electric tail fan for boundary layer ingestion. The dynamic model is compared against an existing steady state design model. An electrical system model using a simple power flow approach is integrated into existing modeling tools used for dynamic simulation of the turbomachinery of the vehicle. In addition to the simple power flow model of the electrical system, a more detailed model is used for comparison at a key vehicle transient flight condition. The controller is a gain scheduled proportional-integral type that is examined throughout the flight envelope for performance metrics such as rise time and operability margins. Potential improvements in efficiency for the vehicle are explored by adjusting the power split between the energy used for thrust by the turbofans and that extracted to supply power to the tail fan. Finally, an operability study of the vehicle is conducted using a 900 nautical mile mission profile for a nominal vehicle configuration, a deteriorated propulsion system at the end of its operating life, and an optimized power schedule with improved efficiency.

Turboelectric↗
NASA NTRS2001

Inferring Instantaneous, Multivariate and Nonlinear Sensitivities for the Analysis of Feedback Processes in a Dynamical System: Lorenz Model Case Study

A new approach is presented for the analysis of feedback processes in a nonlinear dynamical system by observing its variations. The new methodology consists of statistical estimates of the sensitivities between all pairs of variables in the system based on a neural network modeling of the dynamical system. The model can then be used to estimate the instantaneous, multivariate and nonlinear sensitivities, which are shown to be essential for the analysis of the feedbacks processes involved in the dynamical system. The method is described and tested on synthetic data from the low-order Lorenz circulation model where the correct sensitivities can be evaluated analytically.

Aires, Filipe↗
NASA NTRS1993

Synthesis of Optimal Nonlinear Feedback Laws for Dynamic Systems Using Neural Networks

Open-loop solutions of dynamical optimization problems can be numerically computed usingexisting software packages. The computed time histories of the state and control variables, formultiple sets of end conditions can then be used to train a neural network to 'recognize' the optimal,nonlinear feedback relation between the states and controls of the system. The 'learned' network canthen be used to output an approximate optimal control given a full set (or a partial set) of measuredsystem states. With simple neural networks, we have successfully demonstrated the efficacy of theproposed approach using a minimum-time orbit injection problem. The usefulness and limitations ofthis novel approach on real-life optimal guidance and control problems, with many state and control variables as well as path inequality constraints, remain to be seen.

Orbit injection problem↗