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A uniformly controllable and implicit scheme for the 1-D wave equation

Arnaud Münch (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper studies the exact controllability of a finite dimensional system obtained by discretizing in space and time the linear 1-D wave system with a boundary control at one extreme. It is known that usual schemes obtained with finite difference or finite element methods are not uniformly controllable with respect to the discretization parameters h and Δ t . We introduce an implicit finite difference scheme which differs from the usual centered one by additional terms of order h 2 and Δ t 2 . Using a discrete...

A uniformly controllable and implicit scheme for the 1-D wave equation

Arnaud Münch (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper studies the exact controllability of a finite dimensional system obtained by discretizing in space and time the linear 1-D wave system with a boundary control at one extreme. It is known that usual schemes obtained with finite difference or finite element methods are not uniformly controllable with respect to the discretization parameters h and Δt. We introduce an implicit finite difference scheme which differs from the usual centered one by additional terms of order h2 and Δt2. Using...

A variable structure observer for the control of robot manipulators

Abdelkader Abdessameud, Mohamed Khelfi (2006)

International Journal of Applied Mathematics and Computer Science

This paper deals with the application of a variable structure observer developed for a class of nonlinear systems to solve the trajectory tracking problem for rigid robot manipulators. The analyzed approach to observer design proposes a simple design methodology for systems having completely observable linear parts and bounded nonlinearities andor uncertainties. This observer is basically the conventional Luenberger observer with an additional switching term that is used to guarantee robustness...

A vehicle-track-soil dynamic interaction problem in sequential and parallel formulation

Janusz Kogut, Henryk Ciurej (2010)

International Journal of Applied Mathematics and Computer Science

Some problems regarding numerical modeling of predicted vibrations excited by railway traffic are discussed. Model formulation in the field of structural mechanics comprises a vehicle, a track (often in a tunnel) and soil. Time consuming computations are needed to update large matrices at every discrete step. At first, a sequential Matlab code is generated. Later on, the formulation is modified to use grid computing, thereby a significant reduction in computational time is expected.

A weak regularity theorem for real analytic optimal control problems.

Hector J. Sussmann (1986)

Revista Matemática Iberoamericana

We consider real analytic finite-dimensional control problems with a scalar input that enters linearly in the evolution equations. We prove that, whenever it is possible to steer a state x to another state y by means of a measurable control, then it is possible to steer x to y by means of a control that has an extra regularity property, namely, that of being analytic on an open dense subset of its interval of definition. Since open dense sets can have very small measure, this is a very weak property....

Active fault tolerant control of nonlinear systems: The cart-pole example

Marcello Bonfè, Paolo Castaldi, Nicola Mimmo, Silvio Simani (2011)

International Journal of Applied Mathematics and Computer Science

This paper describes the design of fault diagnosis and active fault tolerant control schemes that can be developed for nonlinear systems. The methodology is based on a fault detection and diagnosis procedure relying on adaptive filters designed via the nonlinear geometric approach, which allows obtaining the disturbance de-coupling property. The controller reconfiguration exploits directly the on-line estimate of the fault signal. The classical model of an inverted pendulum on a cart is considered...

Actuator fault tolerance in control systems with predictive constrained set-point optimizers

Piotr M. Marusak, Piotr Tatjewski (2008)

International Journal of Applied Mathematics and Computer Science

Mechanisms of fault tolerance to actuator faults in a control structure with a predictive constrained set-point optimizer are proposed. The structure considered consists of a basic feedback control layer and a local supervisory set-point optimizer which executes as frequently as the feedback controllers do with the aim to recalculate the set-points both for constraint feasibility and economic performance. The main goal of the presented reconfiguration mechanisms activated in response to an actuator...

Adaptive compensators for perturbed positive real infinite-dimensional systems

Ruth Curtain, Michael Demetriou, Kazufumi Ito (2003)

International Journal of Applied Mathematics and Computer Science

The aim of this investigation is to construct an adaptive observer and an adaptive compensator for a class of infinite-dimensional plants having a known exogenous input and a structured perturbation with an unknown constant parameter, such as the case of static output feedback with an unknown gain. The adaptive observer uses the nominal dynamics of the unperturbed plant and an adaptation law based on the Lyapunov redesign method. We obtain conditions on the system to ensure uniform boundedness of...

Adaptive control of cluster-based Web systems using neuro-fuzzy models

Krzysztof Zatwarnicki (2012)

International Journal of Applied Mathematics and Computer Science

A significant development of Web technologies requires the application of more and more complex systems and algorithms for maintaining high quality of Web services. Presently, not only simple decision-making tools but also complex adaptation algorithms using artificial intelligence techniques are applied for controlling HTTP request traffic. The paper presents a new LFNRD (Local Fuzzy-Neural Adaptive Request Distribution) algorithm for request distribution in cluster-based Web systems using neuro-fuzzy...

Adaptive control of uncertain nonholonomic systems in finite time

Jiankui Wang, Guoshan Zhang, Hongyi Li (2009)

Kybernetika

In this paper, the finite-time stabilization problem of chained form systems with parametric uncertainties is investigated. A novel switching control strategy is proposed for adaptive finite-time control design with the help of Lyapunov-based method and time-rescaling technique. With the proposed control law, the uncertain closed-loop system under consideration is finite-time stable within a given settling time. An illustrative example is also given to show the effectiveness of the proposed controller....

Adaptive Parameter Estimation of Hyperbolic Distributed Parameter Systems: Non-symmetric Damping and Slowly Time Varying Systems

H. T. Banks, M. A. Demetriou (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper a model reference-based adaptive parameter estimator for a wide class of hyperbolic distributed parameter systems is considered. The proposed state and parameter estimator can handle hyperbolic systems in which the damping sesquilinear form may not be symmetric (or even present) and a modification to the standard adaptive law is introduced to account for this lack of symmetry (or absence) in the damping form. In addition, the proposed scheme is modified for systems in which the input...

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