Displaying similar documents to “Predictor control for wave PDE / nonlinear ODE cascaded system with boundary value-dependent propagation speed”

The control of drilling vibrations: A coupled PDE-ODE modeling approach

Belem Saldivar, Sabine Mondié, Juan Carlos Avila Vilchis (2016)

International Journal of Applied Mathematics and Computer Science

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The main purpose of this contribution is the control of both torsional and axial vibrations occurring along a rotary oilwell drilling system. The model considered consists of a wave equation coupled to an ordinary differential equation (ODE) through a nonlinear function describing the rock-bit interaction. We propose a systematic method to design feedback controllers guaranteeing ultimate boundedness of the system trajectories and leading consequently to the suppression of harmful dynamics....

Control of the Wave Equation by Time-Dependent Coefficient

Antonin Chambolle, Fadil Santosa (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We study an initial boundary-value problem for a wave equation with time-dependent sound speed. In the control problem, we wish to determine a sound-speed function which damps the vibration of the system. We consider the case where the sound speed can take on only two values, and propose a simple control law. We show that if the number of modes in the vibration is finite, and none of the eigenfrequencies are repeated, the proposed control law does lead to energy decay. We illustrate...

Patterns and Waves Generated by a Subcritical Instability in Systems with a Conservation Law under the Action of a Global Feedback Control

Y. Kanevsky, A.A. Nepomnyashchy (2010)

Mathematical Modelling of Natural Phenomena

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A global feedback control of a system that exhibits a subcritical monotonic instability at a non-zero wavenumber (short-wave, or Turing instability) in the presence of a zero mode is investigated using a Ginzburg-Landau equation coupled to an equation for the zero mode. The method based on a variational principle is applied for the derivation of a low-dimensional evolution model. In the framework of this model the investigation of the ...

The anti-disturbance property of a closed-loop system of 1-d wave equation with boundary control matched disturbance

Xiao-Rui Wang, Gen-Qi Xu (2019)

Applications of Mathematics

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We study the anti-disturbance problem of a 1-d wave equation with boundary control matched disturbance. In earlier literature, the authors always designed the controller such as the sliding mode control and the active disturbance rejection control to stabilize the system. However, most of the corresponding closed-loop systems are boundedly stable. In this paper we show that the linear feedback control also has a property of anti-disturbance, even if the disturbance includes some information...

Comparison of the stability boundary and the frequency response stability condition in learning and repetitive control

Szathys Songschon, Richard Longman (2003)

International Journal of Applied Mathematics and Computer Science

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In iterative learning control (ILC) and in repetitive control (RC) one is interested in convergence to zero tracking error as the repetitions of the command or the periods in the command progress. A condition based on steady state frequency response modeling is often used, but it does not represent the true stability boundary for convergence. In this paper we show how this useful condition differs from the true stability boundary in ILC and RC, and show that in applications of RC the...

Asymptotic stability of wave equations with memory and frictional boundary dampings

Fatiha Alabau-Boussouira (2008)

Applicationes Mathematicae

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This work is concerned with stabilization of a wave equation by a linear boundary term combining frictional and memory damping on part of the boundary. We prove that the energy decays to zero exponentially if the kernel decays exponentially at infinity. We consider a slightly different boundary condition than the one used by M. Aassila et al. [Calc. Var. 15, 2002]. This allows us to avoid the assumption that the part of the boundary where the feedback is active is strictly star-shaped....

Stability analysis of uncertain complex-variable delayed nonlinear systems via intermittent control with multiple switched periods

Song Zheng (2018)

Kybernetika

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In this paper, an intermittent control approach with multiple switched periods is proposed for the robust exponential stabilization of uncertain complex-variable delayed nonlinear systems with parameters perturbation, in which the considered complex systems have bounded parametric uncertainties. Based on the Lyapunov stability theory and comparison theorem of differential equations, some stability criteria are established for a class of uncertain complex delayed nonlinear systems with...

Stability and Instability of Solitary Wave Solutions of a Nonlinear Dispersive System of Benjamin-Bona-Mahony Type

Hakkaev, Sevdzhan (2003)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 35B35, 35B40, 35Q35, 76B25, 76E30. This paper concerns the orbital stability and instability of solitary waves of the system of coupling equations of Benjamin-Bona-Mahony type. By applying the abstract results of Grillakis, Shatah and Strauss and detailed spectral analysis, we obtain the existence and stability of the solitary waves. Partially Supported by Grant MM-810/98 of MESC and by Scientefic Research Grant 19/12.03.2003...

Indirect stabilization of locally coupled wave-type systems

Fatiha Alabau-Boussouira, Matthieu Léautaud (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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We study in an abstract setting the indirect stabilization of systems of two wave-like equations coupled by a localized zero order term. Only one of the two equations is directly damped. The main novelty in this paper is that the coupling operator is not assumed to be coercive in the underlying space. We show that the energy of smooth solutions of these systems decays polynomially at infinity, whereas it is known that exponential stability...