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Sensor network design for the estimation of spatially distributed processes

Dariusz Uciński, Maciej Patan (2010)

International Journal of Applied Mathematics and Computer Science

In a typical moving contaminating source identification problem, after some type of biological or chemical contamination has occurred, there is a developing cloud of dangerous or toxic material. In order to detect and localize the contamination source, a sensor network can be used. Up to now, however, approaches aiming at guaranteeing a dense region coverage or satisfactory network connectivity have dominated this line of research and abstracted away from the mathematical description of the physical...

Sensor network scheduling for identification of spatially distributed processes

Dariusz Uciński (2012)

International Journal of Applied Mathematics and Computer Science

The work treats the problem of fault detection for processes described by partial differential equations as that of maximizing the power of a parametric hypothesis test which checks whether or not system parameters have nominal values. A simple node activation strategy is discussed for the design of a sensor network deployed in a spatial domain that is supposed to be used while detecting changes in the underlying parameters which govern the process evolution. The setting considered relates to a...

Sensors and boundary state reconstruction of hyperbolic systems

El Hassan Zerrik, Hamid Bourray, Samir Ben Hadid (2010)

International Journal of Applied Mathematics and Computer Science

This paper deals with the problem of regional observability of hyperbolic systems in the case where the subregion of interest is a boundary part of the system evolution domain. We give a definition and establish characterizations in connection with the sensor structure. Then we show that it is possible to reconstruct the system state on a subregion of the boundary. The developed approach, based on the Hilbert uniqueness method (Lions, 1988), leads to a reconstruction algorithm. The obtained results...

Shape optimization for a time-dependent model of a carousel press in glass production

Petr Salač, Jan Stebel (2019)

Applications of Mathematics

This contribution presents the shape optimization problem of the plunger cooling cavity for the time dependent model of pressing the glass products. The system of the mould, the glass piece, the plunger and the plunger cavity is considered in four consecutive time intervals during which the plunger moves between 6 glass moulds. The state problem is represented by the steady-state Navier-Stokes equations in the cavity and the doubly periodic energy equation in the whole system, under the assumption...

Shape optimization of piezoelectric sensors or actuators for the control of plates

Emmanuel Degryse, Stéphane Mottelet (2005)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with a new method to control flexible structures by designing non-collocated sensors and actuators satisfying a pseudo-collocation criterion in the low-frequency domain. This technique is applied to a simply supported plate with a point force actuator and a piezoelectric sensor, for which we give some theoretical and numerical results. We also compute low-order controllers which stabilize pseudo-collocated systems and the closed-loop behavior show that this approach is very promising....

Shape optimization of piezoelectric sensors or actuators for the control of plates

Emmanuel Degryse, Stéphane Mottelet (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with a new method to control flexible structures by designing non-collocated sensors and actuators satisfying a pseudo-collocation criterion in the low-frequency domain. This technique is applied to a simply supported plate with a point force actuator and a piezoelectric sensor, for which we give some theoretical and numerical results. We also compute low-order controllers which stabilize pseudo-collocated systems and the closed-loop behavior show that this approach is very promising. ...

Sharp regularity of the second time derivative w_tt of solutions to Kirchhoff equations with clamped Boundary Conditions

Irena Lasiecka, Roberto Triggiani (2001)

International Journal of Applied Mathematics and Computer Science

We consider mixed problems for Kirchhoff elastic and thermoelastic systems, subject to boundary control in the clamped Boundary Conditions B.C. (“clamped control”). If w denotes elastic displacement and θ temperature, we establish optimal regularity of {w, w_t, w_tt} in the elastic case, and of {w, w_t, w_tt, θ} in the thermoelastic case. Our results complement those presented in (Lagnese and Lions, 1988), where sharp (optimal) trace regularity results are obtained for the corresponding boundary...

Simultaneous controllability in sharp time for two elastic strings

Sergei Avdonin, Marius Tucsnak (2001)

ESAIM: Control, Optimisation and Calculus of Variations

We study the simultaneously reachable subspace for two strings controlled from a common endpoint. We give necessary and sufficient conditions for simultaneous spectral and approximate controllability. Moreover we prove the lack of simultaneous exact controllability and we study the space of simultaneously reachable states as a function of the position of the joint. For each type of controllability result we give the sharp controllability time.

Simultaneous controllability in sharp time for two elastic strings

Sergei Avdonin, Marius Tucsnak (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We study the simultaneously reachable subspace for two strings controlled from a common endpoint. We give necessary and sufficient conditions for simultaneous spectral and approximate controllability. Moreover we prove the lack of simultaneous exact controllability and we study the space of simultaneously reachable states as a function of the position of the joint. For each type of controllability result we give the sharp controllability time.

Some decay properties for the damped wave equation on the torus

Nalini Anantharaman, Matthieu Léautaud (2012)

Journées Équations aux dérivées partielles

This article is a proceedings version of the ongoing work [1], and has been the object of a talk of the second author during the Journées “Équations aux Dérivées Partielles” (Biarritz, 2012).We address the decay rates of the energy of the damped wave equation when the damping coefficient b does not satisfy the Geometric Control Condition (GCC). First, we give a link with the controllability of the associated Schrödinger equation. We prove that the observability of the Schrödinger group implies that...

Some new results related to the null controllability of the 1 - d heat equation

Antonio López, Enrique Zuazua (1997/1998)

Séminaire Équations aux dérivées partielles

We address three null controllability problems related to the 1 - d heat equation. First we show that the 1 - d heat equation with a rapidly oscillating density is uniformly null controllable as the period of the density tends to zero. We also prove that the same result holds for the finite-difference semi-discretization in space of the constant coefficient heat equation as the step size tends to zero. Finally, we prove that the null controllability of the constant coefficient heat equation can be obtained...

Some uniqueness and observability problems arising in the control of vibrations

Enrique Zuazua (1999)

Journées équations aux dérivées partielles

We discuss a control problem for the Lamé system which naturally leads to the following uniqueness problem: Given a bounded domain of 𝐑 3 , are there non-trivial solutions of the evolution Lamé system with homogeneous Dirichlet boundary conditions for which the first two components vanish? We show that such solutions do not exist when the domain is Lipschitz. However, in two space dimensions one can build easily polygonal domains in which there are eigenvibrations with the first component being identically...

Source localization and sensor placement in environmental monitoring

Alexander Khapalov (2010)

International Journal of Applied Mathematics and Computer Science

In this paper we discuss two closely related problems arising in environmental monitoring. The first is the source localization problem linked to the question How can one find an unknown "contamination source"? The second is an associated sensor placement problem: Where should we place sensors that are capable of providing the necessary "adequate data" for that? Our approach is based on some concepts and ideas developed in mathematical control theory of partial differential equations.

Spatial compensation of boundary disturbances by boundary actuators

Larbi Afifi, Abdelhakim Chafiai, Abdelhaq El Jai (2001)

International Journal of Applied Mathematics and Computer Science

In this paper we show how to find convenient boundary actuators, termed boundary efficient actuators, ensuring finite-time space compensation of any boundary disturbance. This is the so-called remediability problem. Then we study the relationship between this remediability notion and controllability by boundary actuators, and hence the relationship between boundary strategic and boundary efficient actuators. We also determine the set of boundary remediable disturbances, and for a boundary disturbance,...

Currently displaying 341 – 360 of 441