Modeling, Simulation and Control of Nonlinar Engineering Dynamical Systems

Dynamic Systems Biology Modeling and Simulation
Free download. Book file PDF easily for everyone and every device. You can download and read online Modeling, Simulation and Control of Nonlinar Engineering Dynamical Systems file PDF Book only if you are registered here. And also you can download or read online all Book PDF file that related with Modeling, Simulation and Control of Nonlinar Engineering Dynamical Systems book. Happy reading Modeling, Simulation and Control of Nonlinar Engineering Dynamical Systems Bookeveryone. Download file Free Book PDF Modeling, Simulation and Control of Nonlinar Engineering Dynamical Systems at Complete PDF Library. This Book have some digital formats such us :paperbook, ebook, kindle, epub, fb2 and another formats. Here is The CompletePDF Book Library. It's free to register here to get Book file PDF Modeling, Simulation and Control of Nonlinar Engineering Dynamical Systems Pocket Guide.

Contents:

  • Recommended for you
  • Dynamic Systems: Modeling, Simulation, and Control
  • 1st Edition
  • Thanks for helping keep SourceForge clean.
  • Modelling, Simulation, and Control of Non-Linear Dynamical Systems

    • Select the China site in Chinese or English for best site performance. Other MathWorks country sites are not optimized for visits from your location.

    Recommended for you

    Extracting sparse high-dimensional dynamics from limited data. There are several reasons for this behavior: first, this pseudo-Lyapunov exponent does depend on time and initial conditions whereas the classical Lyapunov exponent does not ergodicity. This data are then used to construct a nonlinear surrogate model with established data fitting techniques such as neural networks, radial basis networks, echo state networks, or wavelet networks [ 5 , 6 ]. The presented methodology is advantageous mainly due to the possibility of considering Preface xv various effects of rotation that cannot be introduced in the commercial FEM codes. Case 1.

    This website uses cookies to improve your user experience, personalize content and ads, and analyze website traffic. By continuing to use this website, you consent to our use of cookies. Toggle Main Navigation. Lamarque 8 6 4 2 -9 -8 -7 -6 z0 Fig.

    Dynamic Systems: Modeling, Simulation, and Control

    Finally, we want to highlight the fact that these results can be generalized to non-smooth systems. This Lyapunov exponent can be defined using matrices of passage and matrices of jump, see [13, 16]. This makes it possible to define and calculate the spectrum of finite-time pseudo-Lyapunov exponents. For example, considering an impact linear oscillator see Fig.

    The matrices of passage and jump can thus be written, see [16]. It is possible to bound this divergence on every part of the path, that is to say every matrix Ji or Si.

    Chapters in Books

    But in this case, the bound obtained may be too coarse see [17]. Lamarque 15 10 5 0 1 0 2 3 4 5 1 -5 2 3 4 5 Fig. Here, the consequences of this phenomenon are even worse than in the smooth case, because of the grazing bifurcation.

    1. Nav view search.
    2. Fireworks: A Gunsite Anthology?
    3. Associated Data.
    4. International Conference on Modeling, Simulation and Control ICMSC !
    5. Essential financial techniques for hospitality managers?
    6. JMCAD - modeling of dynamic systems!

    Indeed, this case where the speed of impact on the wall is equal to zero, is challenging: the matrix of jump has got a term that tends to infinity and the behavior of the system is complicated see [18, 19]. The method is also often used to quantify the finitetime response of a dynamical system if uncertainties exist. For a transient behavior and the practical study of divergence or stability, we look for another estimation that could lead to bounds for tangent behavior. That is why finite-time pseudo-Lyapunov exponents have been computed in continuous cases and discrete ones.

    In all these studies, the conclusions have always been that they may be superior to the Lyapunov exponent. Particularly, they may be positive whereas the Lyapunov exponent is negative. This does not mean that the domain of parameters concerned by chaos is extended.

    Indeed, chaos is predicted in an infinite time. Here, we just deal with finite-time and we highlight the fact that this indicator called a finite-time pseudo-Lyapunov exponent makes it possible to bound the tangent finite-time divergence of a dynamical system with initial conditions known with finite accuracy, and numerical calculations made with strictly positive small step of time. This indicator is mainly a bound to quantify finite-time maximum of instability. A way to go further in this study would be to examine the influence of time and initial conditions on the Lyapunov exponent of higher derivatives [20].

    1st Edition

    The general problem of the stability of motion. International Journal of Control, 55 3 —, A multiplicative ergodic theorem: Lyapunov characteristic numbers for dynamical systems. Transactions of the Moscow Mathematical Society, —, Wolf, J. Swift, H. Swinney, and J. Determining Lyapunov exponents from a time series.

    Physica D: Nonlinear Phenomena, 16 3 —, Udwadia and H. An efficient and stable approach for computation of Lyapunov characteristic exponents of continuous dynamical systems. Applied Mathematics and Computation, 2—3 —, Ramasubramanian and M. A comparative study of computation of Lyapunov spectra with different algorithms. Physica D: Nonlinear Phenomena, 1—2 —86, Tancredi, A. A comparison between methods to compute Lyapunov exponents. Astronomical Journal, 2 —, Ding and J.

    Nonlinear finite-time Lyapunov exponent and predictability. Physics Letters A, 5 —, Aurell, G. Boffetta, A.

    Availability

    Crisanti, G. Paladin, and A.

    • Applications of Sliding Mode Control?
    • Semantic mining technologies for multimedia databases?
    • Top Authors.
    • Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems!
    • Modeling, Simulation and Control of Nonlinear Engineering Dynamical Systems!
    • Model selection for hybrid dynamical systems via sparse regression!
    • Complex Systems: Relationships between Control, Communications and Computing?

    Growth of non-infinitesimal perturbations in turbulence. Physical Review Letters, 77 7 —, Quantifying local predictability in phase space.

    1. Book Modeling Simulation And Control Of Nonlinar Engineering Dynamical Systems !
    2. Year in Focus 2010 [Getty Images]?
    3. Chapters in Books!
    4. Dynamical system - Wikipedia!
    5. Description.
    6. Dynamic Systems: Modeling, Simulation, and Control!

    Physica D: Nonlinear Phenomena, 35 1—2 —, Nicolis, S. Vannitsem, and J. Short-range predictability of the atmosphere: mechanisms for superexponential error growth. Quarterly Journal — Royal Meteorological Society, —, Hinrichs, M.

    Digitally Programmable Analog Computer for Non-linear Dynamical Systems

    Oestreich, and K. Dynamics of oscillators with impact and friction. Jin, Q. Lu, and E. A method for calculating the spectrum of Lyapunov exponents by local maps in non-smooth impact-vibrating systems. Journal of Sound and Vibration, 4—5 —, Calculation of Lyapunov exponents for dynamic systems with discontinuities. Estimation of the dominant Lyapunov exponent of non-smooth systems on the basis of maps synchronization.

    Wu and N. International Journal of Non-linear Mechanics, 36 7 — , Computation of the solutions of the Fokker-Planck equation for one and two dof systems. Communications in Nonlinear Science and Numerical Simulation, 74 — Un indicateur pour optimiser les calculs trajectographiques. The dynamics of systems near to grazing collision. Journal of Applied Mathematics and Mechanics, 58 3 —, Janin and C. Stability of singular periodic motions in a vibro-impact oscillator.

    Nonlinear Dynamics, 28 3—4 —, Dressler and J. Generalized Lyapunov exponents corresponding to higher derivatives. Physica D: Nonlinear Phenomena, 59 4 —, Numerical Characterization of the Chaotic Nonregular Dynamics of Pseudoelastic Oscillators Davide Bernardini and Giuseppe Rega 1 Introduction Previous studies on the nonlinear dynamics of pseudoelastic oscillators showed the occurrence of chaotic responses in some ranges of the system parameters [1,2]. The restoring force was modeled by a thermomechanically consistent model with four state variables [3].

    In comparison with the simpler polynomial constitutive laws considered for example in [4], the present model is characterized by more governing parameters and it is therefore interesting to understand whether nonregular responses only occur in isolated zones or are actually robust outcomes. The relevant analyses need to be carried out through some synthetic measure of non-regularity that has to be reliable and computationally simple in order to allow for systematic investigations in meaningful parameter spaces.

    Whereas the numerical characterization of chaos in smooth dynamical systems is often carried out via the computation of Lyapunov exponents, in the present case the computation of such exponents, following, for example [5], does not seem to be a convenient strategy. The attention has thus been focused on the simpler direct numerical tool represented by the method of wandering trajectories [6].

    Thanks for helping keep SourceForge clean.

    This volume contains the invited papers presented at the 9th International Conference "Dynamical Systems — Theory and Applications" held in Lódz, Poland. All errors and omissions excepted. J. Awrejcewicz (Ed.) Modeling, Simulation and Control of Nonlinear Engineering · Dynamical Systems. State-of-the-Art.

    The method is based on the numerical evaluation of the separation between pairs of neighboring trajectories normalized with respect to a suitable measure of the motion amplitude. Such normalized perturbations provide a tool to detect the occurrence of nonregular and chaotic responses. The method has been successfully applied in the literature to estimate regular and chaotic responses for non-smooth mechanical oscillators with up to two degrees of freedom [7].

    Bernardini, G. Rega The purpose of this paper is to calibrate and validate the method of wandering trajectories within a thermomechanical framework and to present some results on the overall characterization of the chaotic response of pseudoelastic oscillators. The model used for the restoring force fits into the family of models introduced in [3] that are derived from the assignment of two constitutive functions: the free energy and the dissipation function.

    The specific version used in this work has been introduced in [1] and is characterized by a new form for the dissipation function with respect to those in [3]. However, once activated, each kind of behavior is smooth. The initial conditions i. The basic idea is very simple: a motion is classified as non-regular if the separation with a neighboring trajectory starting from an admissible state overcomes a given threshold. Of course, a key issue is the proper definition of the auxiliary trajectory and of the threshold.

    More specifically, trajectories initiated from two nearby points on a chaotic attractor separate away from each other until the separation levels off at the size of the attractor.

    Modelling, Simulation, and Control of Non-Linear Dynamical Systems

    Rega This test certainly detects the sensitivity to initial conditions of the trajectory. However this is only a necessary but not sufficient condition for the motion to be chaotic. In facts, the sensitivity to initial conditions alone only indicates that the perturbation may have taken the trajectory outside the basin of attraction of the attractor.