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Optimizing the linear quadratic minimum-time problem for discrete distributed systems

Mostafa Rachik, Ahmed Abdelhak (2002)

International Journal of Applied Mathematics and Computer Science

With reference to the work of Verriest and Lewis (1991) on continuous finite-dimensional systems, the linear quadratic minimum-time problem is considered for discrete distributed systems and discrete distributed time delay systems. We treat the problem in two variants, with fixed and free end points. We consider a cost functional J which includes time, energy and precision terms, and then we investigate the optimal pair (N, u) which minimizes J.

Protector control: Extension to a class of nonlinear distributed systems

Youssef Qaraai, Abdes Samed Bernoussi (2010)

International Journal of Applied Mathematics and Computer Science

We present an extension of the protector control scheme introduced for the linear case in a previous work to a class of nonlinear systems. The systems considered are assumed to have a finite propagation velocity while the initial state is subject to a spreading disturbance. We characterize such a control first by using the remediability approach to the resulting nonlinear delay system, and then by coupling families of transformations and the delay approach. To illustrate this work, we provide a...

Realization theory methods for the stability investigation of nonlinear infinite-dimensional input-output systems

Volker Reitmann (2011)

Mathematica Bohemica

Realization theory for linear input-output operators and frequency-domain methods for the solvability of Riccati operator equations are used for the stability and instability investigation of a class of nonlinear Volterra integral equations in a Hilbert space. The key idea is to consider, similar to the Volterra equation, a time-invariant control system generated by an abstract ODE in a weighted Sobolev space, which has the same stability properties as the Volterra equation.

Regional observation and sensors

Abdelhaq El Jai, Houria Hamzaoui (2009)

International Journal of Applied Mathematics and Computer Science

The purpose of this short paper is to provide original results related to the choice of the number of sensors and their supports for general distributed parameter systems. We introduce the notion of extended sensors and we show that the observation error decreases when the support of a sensor is widened. We also show that the observation error decreases when the number of sensors increases.

Resolvent estimates in controllability theory and applications to the discrete wave equation

Sylvain Ervedoza (2009)

Journées Équations aux dérivées partielles

We briefly present the difficulties arising when dealing with the controllability of the discrete wave equation, which are, roughly speaking, created by high-frequency spurious waves which do not travel. It is by now well-understood that such spurious waves can be dealt with by applying some convenient filtering technique. However, the scale of frequency in which we can guarantee that none of these non-traveling waves appears is still unknown in general. Though, using Hautus tests, which read the...

Stabilization of second order evolution equations by a class of unbounded feedbacks

Kais Ammari, Marius Tucsnak (2001)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we consider second order evolution equations with unbounded feedbacks. Under a regularity assumption we show that observability properties for the undamped problem imply decay estimates for the damped problem. We consider both uniform and non uniform decay properties.

Stabilization of second order evolution equations by a class of unbounded feedbacks

Kais Ammari, Marius Tucsnak (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we consider second order evolution equations with unbounded feedbacks. Under a regularity assumption we show that observability properties for the undamped problem imply decay estimates for the damped problem. We consider both uniform and non uniform decay properties.

Strong stabilization of controlled vibrating systems

Jean-François Couchouron (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with feedback stabilization of second order equations of the form ytt + A0y + u (t) B0y (t) = 0, t ∈ [0, +∞[, where A0 is a densely defined positive selfadjoint linear operator on a real Hilbert space H, with compact inverse and B0 is a linear map in diagonal form. It is proved here that the classical sufficient ad-condition of Jurdjevic-Quinn and Ball-Slemrod with the feedback control u = ⟨yt, B0y⟩H implies the strong stabilization. This result is derived from a general compactness...

Strong stabilization of controlled vibrating systems

Jean-François Couchouron (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with feedback stabilization of second order equations of the form ytt + A0y + u (t) B0y (t) = 0, t ∈ [0, +∞[, where A0 is a densely defined positive selfadjoint linear operator on a real Hilbert space H, with compact inverse and B0 is a linear map in diagonal form. It is proved here that the classical sufficient ad-condition of Jurdjevic-Quinn and Ball-Slemrod with the feedback control u = ⟨yt, B0y⟩H implies the strong stabilization. This result is derived from a general compactness theorem...

Sturm-Liouville systems are Riesz-spectral systems

Cédric Delattre, Denis Dochain, Joseph Winkin (2003)

International Journal of Applied Mathematics and Computer Science

The class of Sturm-Liouville systems is defined. It appears to be a subclass of Riesz-spectral systems, since it is shown that the negative of a Sturm-Liouville operator is a Riesz-spectral operator on L^2(a,b) and the infinitesimal generator of a C_0-semigroup of bounded linear operators.

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