Search results for "YAP"
showing 10 items of 268 documents
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…
Perturbation of the Lyapunov spectra of periodic orbits
2012
We describe all Lyapunov spectra that can be obtained by perturbing the derivatives along periodic orbits of a diffeomorphism. The description is expressed in terms of the finest dominated splitting and Lyapunov exponents that appear in the limit of a sequence of periodic orbits, and involves the majorization partial order. Among the applications, we give a simple criterion for the occurrence of universal dynamics.
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…
Exponential Transients in Continuous-Time Symmetric Hopfield Nets
2001
We establish a fundamental result in the theory of continuous-time neural computation, by showing that so called continuous-time symmetric Hopfield nets, whose asymptotic convergence is always guaranteed by the existence of a Liapunov function may, in the worst case, possess a transient period that is exponential in the network size. The result stands in contrast to e.g. the use of such network models in combinatorial optimization applications. peerReviewed
Local Capacity $H_{\infty}$ Control for Production Networks of Autonomous Work Systems With Time-Varying Delays
2010
This paper considers the problem of local capacity H∞ control for a class of production networks of autonomous work systems with time-varying delays in the capacity changes. The system under consideration is modeled in a discrete-time singular form. Attention is focused on the design of a controller gain for the local capacity adjustments which maintains the work-in-progress (WIP) in each work system in the vicinity of planned levels and guarantees the asymptotic stability of the system and reduces the effect of the disturbance input on the controlled output to a prescribed level. In terms of a matrix inequality, a sufficient condition for the solvability of this problem is presented using …
A Lyapunov–Razumikhin approach for stability analysis of logistics networks with time-delays
2012
Logistics network represents a complex system where different elements that are logistic locations interact with each other. This interaction contains delays caused by time needed for delivery of the material. Complexity of the system, time-delays and perturbations in a customer demand may cause unstable behaviour of the network. This leads to the loss of the customers and high inventory costs. Thus the investigation of the network on stability is desired during its design. In this article we consider local input-to-state stability of such logistics networks. Their behaviour is described by a functional differential equation with a constant time-delay. We are looking for verifiable conditio…
Linear flux observers for induction motors with quadratic Lyapunov certificates
2016
International audience; We propose a full order Linear Time-Varying (LTV) Luenberger observer for the rotor flux estimation of an induction motor. Introducing a suitable reduced-order Linear-Time-Invariant (LTI) system that is always observable and controllable, we show that any arbitrary LTI design and its quadratic Lyapunov certificates can be lifted to the higher-order original LTV dynamics obtaining the same certificates. As a result, we show that arbitrary global uniform exponential bounds can be imposed on the estimation error, regardless of the rotor speed. Then applying a suitable order reduction technique, we build a reduced observer providing the same guarantees. We also establish…
Stability analysis for stochastic hybrid systems: A survey
2014
This survey addresses stability analysis for stochastic hybrid systems (SHS), which are dynamical systems that combine continuous change and instantaneous change and that also include random effects. We re-emphasize the common features found in most of the models that have appeared in the literature, which include stochastic switched systems, Markov jump systems, impulsive stochastic systems, switching diffusions, stochastic impulsive systems driven by renewal processes, diffusions driven by Lévy processes, piecewise-deterministic Markov processes, general stochastic hybrid systems, and stochastic hybrid inclusions. Then we review many of the stability concepts that have been studied, inclu…
A new fuzzy robust dynamic controller for autonomous vehicles with nonholonomic constraints
2005
Abstract In this paper a novel algorithm with a dynamic fuzzy controller applied to the control of trajectory of vehicles with two independent wheels is proposed. An automatic control of trajectory of a vehicle can behave in a not efficient way. It is necessary to consider the friction of the actuators and possible perturbations coming from the outside environment, as for instance the variable characteristics of the ground where the vehicle moves. These perturbations, which depend also on the contact between the wheel and the ground, involve violations of nonholonomic constraints. Thus it is necessary to compensate for these perturbations to obtain a robust control system. The controller sy…
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…