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    Wyświetlanie 1-3 z 3
    Tytuł:
    On the region of attraction of dynamical systems: Application to Lorenz equations
    Autorzy:
    Hammami, M. A.
    Rettab, N. H.
    Powiązania:
    https://bibliotekanauki.pl/articles/229791.pdf
    Data publikacji:
    2020
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    nonlinear dynamical systems
    Lyapunov function
    basin of attraction
    Lorenz equations
    Opis:
    Many nonlinear dynamical systems can present a challenge for the stability analysis in particular the estimation of the region of attraction of an equilibrium point. The usual methodis based on Lyapunov techniques. For the validity of the analysis it should be supposed that the initial conditions lie in the domain of attraction. In this paper, we investigate such problem for a class of dynamical systems where the origin is not necessarily an equilibrium point. In this case, a small compact neighborhood of the origin can be estimated as an attractor for the system. We give a method to estimate the basin of attraction based on the construction of a suitable Lyapunov function. Furthermore, an application to Lorenz system is given to verify the effectiveness of the proposed method.
    Źródło:
    Archives of Control Sciences; 2020, 30, 3; 389-409
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Implementation of the chaotic mobile robot for the complex missions
    Autorzy:
    Fahmy, A. A.
    Powiązania:
    https://bibliotekanauki.pl/articles/384403.pdf
    Data publikacji:
    2012
    Wydawca:
    Sieć Badawcza Łukasiewicz - Przemysłowy Instytut Automatyki i Pomiarów
    Tematy:
    chaos
    chaotic motion
    chaotic mobile robot
    Chua's circuit
    Arnold and Lorenz equations
    Opis:
    Mobile robotics, after decades of continuous development, keeps up as an intensive research issue because of its ever- increasing application to different domains and its economical and technological relevance. Interesting applications can be seen in robots performing floor-cleaning tasks, executing industrial transportation, exploring volcanoes, scanning areas to find explosive devices, and so on. a chaotic signal for an autonomous mobile robot is to increase and to take advantage of coverage areas resulting from its travelling paths. The chaotic behavior of the mobile robot is achieved by adding nonlinear equations into the robot kinematic equations, like Arnold, Lorenz, and Chua’s equations, that are well known equations for had a chaotic behavior. The performance of the three guiding signals for robotics system is evaluated in the sense of the wide area coverage, the evenness index, and the total trajectory distance.
    Źródło:
    Journal of Automation Mobile Robotics and Intelligent Systems; 2012, 6, 2; 8-12
    1897-8649
    2080-2145
    Pojawia się w:
    Journal of Automation Mobile Robotics and Intelligent Systems
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Evolution equations in ostensible metric spaces: First-order evolutions of nonsmooth sets with nonlocal terms
    Autorzy:
    Lorenz, Thomas
    Powiązania:
    https://bibliotekanauki.pl/articles/729470.pdf
    Data publikacji:
    2008
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    mutational equations
    quasidifferential equations
    funnel equations
    nonlocal geometric evolutions
    reachable sets of differential inclusions
    sets of positive erosion
    sets of positive reach
    Opis:
    Similarly to quasidifferential equations of Panasyuk, the so-called mutational equations of Aubin provide a generalization of ordinary differential equations to locally compact metric spaces. Here we present their extension to a nonempty set with a possibly nonsymmetric distance. In spite of lacking any linear structures, a distribution-like approach leads to so-called right-hand forward solutions.
    These extensions are mainly motivated by compact subsets of the Euclidean space whose evolution is determined by the nonlocal properties of both the current set and the normal cones at its topological boundary. Indeed, simple deformations such as isotropic expansions exemplify that topological boundaries do not have to evolve continuously in time and thus Aubin's original concept cannot be applied directly. Here neither regularity assumptions about the boundaries nor the inclusion principle are required. The regularity of compact reachable sets of differential inclusions is studied extensively instead.
    This example of nonlocal set evolutions in the Euclidean space serves as an introductory motivation for extending ordinary differential equations (and evolution equations) beyond the traditional border of vector spaces - and for combining it with other examples in systems.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2008, 28, 1; 15-73
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-3 z 3

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