Search results for "nonlinear"
showing 10 items of 3684 documents
Invariant varieties of discontinuous vector fields
2004
We study the geometric qualitative behaviour of a class of discontinuous vector fields in four dimensions around typical singularities. We are mainly interested in giving the conditions under which there exist one-parameter families of periodic orbits (a result that can be seen as one analogous to the Lyapunov centre theorem). The focus is on certain discontinuous systems having some symmetric properties. We also present an algorithm which detects and computes periodic orbits.
Neural Petri Control: an application on a mobile robot
2006
In the present work, an innovative nonlinear controller of nonholonomic mechanical systems, characterized by a dynamic not well known model a priori, using a new neural model obtained by the combination of a Petri net with a neural network, is proposed. The performances of the control algorithm are evaluated for tasks of tracking of time trajectories. The study of the stability of the total system to closed loop is based on the Lyapunov theory. Simulation experiments, made taking into consideration a nonholonomic mobile robot, to two wheels, allowed to verify the theoretical results.
The Lyapunov dimension formula for the global attractor of the Lorenz system
2015
The exact Lyapunov dimension formula for the Lorenz system has been analytically obtained first due to G.A.Leonov in 2002 under certain restrictions on parameters, permitting classical values. He used the construction technique of special Lyapunov-type functions developed by him in 1991 year. Later it was shown that the consideration of larger class of Lyapunov-type functions permits proving the validity of this formula for all parameters of the system such that all the equilibria of the system are hyperbolically unstable. In the present work it is proved the validity of the formula for Lyapunov dimension for a wider variety of parameters values, which include all parameters satisfying the …
Observer-based H∞ control on stochastic nonlinear systems with time-delay and actuator nonlinearity
2013
Abstract In this paper, an observer-based H ∞ controller is designed for a class of extended Markov jump systems subject to time-delay and actuator saturation nonlinearity. Gradient linearization procedure is employed to describe such nonlinear systems by several linear Markov jump systems. Next, a mode-dependent Lyapunov function is constructed for these linear systems, and a sufficient condition is derived to make them stochastically stable, and then, a continuous gain-scheduled approach is applied to design a continuous nonlinear observer-based controller on the entire extended nonlinear jump system. A simulation example is given to illustrate the effectiveness of developed techniques.
Dynamics of the Shapovalov mid-size firm model
2020
Forecasting and analyses of the dynamics of financial and economic processes such as deviations of macroeconomic aggregates (GDP, unemployment, and inflation) from their long-term trends, asset markets volatility, etc., are challenging because of the complexity of these processes. Important related research questions include, first, how to determine the qualitative properties of the dynamics of these processes, namely, whether the process is stable, unstable, chaotic (deterministic), or stochastic; and second, how best to estimate its quantitative indicators including dimension, entropy, and correlation characteristics. These questions can be studied both empirically and theoretically. In t…
A nonlinear observer for rotor flux estimation considering magnetic saturation effects in induction motor drives
2015
This paper proposes a non-linear observer for In- duction Machine (IM) drives which takes into consideration the saturation effects. The non-linear observer is based on an original formulation of the dynamic model of the IM taking into consideration the magnetic saturation of the iron core. A Lyapunov based convergence analysis is proposed in order to suitably compute the observer gain guaranteeing the stability of the observer. The proposed non-linear observer has been tested in numerical simulation and experimentally on a suitably developed test set-up. Its behaviour has been compared to that obtained with a classic Full-Order Luenberger Observer (FOLO) in variable flux working conditions…
A Nonlinear Observer for Rotor Flux Estimation of Induction Motor Considering the Estimated Magnetization Characteristic
2017
This paper proposes a nonlinear observer for induction machine drives based on space-vector dynamic model of induction machine, expressed in state form, which presents the peculiarity of taking into consideration the magnetic saturation of the iron core. This observer is particularly suitable in order to obtain high accuracy in rotor flux estimation, in both amplitude and phase position, during working conditions characterized by varying flux, among which the most important are those during electrical losses minimization. A Lyapunov-based convergence analysis is proposed in order to suitably compute the numerical observer gain guaranteeing the convergence of the estimation error. The propos…
Study of irregular dynamics in an economic model: attractor localization and Lyapunov exponents
2021
Cyclicity and instability inherent in the economy can manifest themselves in irregular fluctuations, including chaotic ones, which significantly reduces the accuracy of forecasting the dynamics of the economic system in the long run. We focus on an approach, associated with the identification of a deterministic endogenous mechanism of irregular fluctuations in the economy. Using of a mid-size firm model as an example, we demonstrate the use of effective analytical and numerical procedures for calculating the quantitative characteristics of its irregular limiting dynamics based on Lyapunov exponents, such as dimension and entropy. We use an analytical approach for localization of a global at…
Numerical analysis of dynamical systems: unstable periodic orbits, hidden transient chaotic sets, hidden attractors, and finite-time Lyapunov dimensi…
2018
In this article, on the example of the known low-order dynamical models, namely Lorenz, Rossler and Vallis systems, the difficulties of reliable numerical analysis of chaotic dynamical systems are discussed. For the Lorenz system, the problems of existence of hidden chaotic attractors and hidden transient chaotic sets and their numerical investigation are considered. The problems of the numerical characterization of a chaotic attractor by calculating finite-time time Lyapunov exponents and finite-time Lyapunov dimension along one trajectory are demonstrated using the example of computing unstable periodic orbits in the Rossler system. Using the example of the Vallis system describing the El…
Control of uncertain highly nonlinear biological process based on Takagi–Sugeno fuzzy models
2015
This note deals with the control of uncertain highly nonlinear biological processes. Indeed, an adaptive fuzzy control (AFC) scheme is developed for the pre-treatment of wastewater represented by a Takagi-Sugeno (TS) fuzzy model. The proposed approach uses a fuzzy system to approximate the unknown substrate consumption rate in designing the adaptive controller, and then an observer is designed to estimate the concentration in substrate at the outlet bioreactor. The observer is employed to generate an error signal for the adaptive control law which permits to minimize the influence of the measurement noise on the estimation of the substrate concentration. An update of the fuzzy models parame…