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1
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An output controllability problem for semilinear distributed hyperbolic systems

100%
Zerrik E., Larhrissi R., Bourray H.
International Journal of Applied Mathematics and Computer Science
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2007
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tom 17
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nr 4
437-448
EN
The paper aims at extending the notion of regional controllability developed for linear systems cite to the semilinear hyperbolic case. We begin with an asymptotically linear system and the approach is based on an extension of the Hilbert uniqueness method and Schauder's fixed point theorem. The analytical case is then tackled using generalized inverse techniques and converted to a fixed point problem leading to an algorithm which is successfully implemented numerically and illustrated with examples.
2
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Regional observation and sensors

100%
El Jai A., Hamzaoui H.
International Journal of Applied Mathematics and Computer Science
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2009
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tom 19
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nr 1
5-14
EN
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.
3
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The gradient projection method for solving an optimal control problem

100%
Farag M. H.
Applicationes Mathematicae
|
1996-1997
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tom 24
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nr 2
141-147
EN
A gradient method for solving an optimal control problem described by a parabolic equation is considered. The gradient projection method is applied to solve the problem. The convergence of the projection algorithm is investigated.
4
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Mobile sensor routing for parameter estimation of distributed systems using the parallel tunneling method

88%
Zięba T., Uciński D.
International Journal of Applied Mathematics and Computer Science
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2008
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tom 18
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nr 3
307-318
EN
The paper deals with the problem of optimal path planning for a sensor network with mutliple mobile nodes, whose measurements are supposed to be primarily used to estimate unknown parameters of a system modelled by a partial differential equation. The adopted framework permits to consider two- or three-dimensional spatial domains and correlated observations. Since the aim is to maximize the accuracy of the estimates, a general functional defined on the relevant Fisher information matrix is used as the design criterion. Central to the approach is the parameterization of the sensor trajectories based on cubic B-splines. The resulting finite-dimensional global optimization problem is then solved using a parallel version of the tunneling algorithm. A numerical example is included to clearly demonstrate the idea presented in the paper.
5
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An integrodifferential approach to modeling, control, state estimation and optimization for heat transfer systems

75%
Rauh A., Senkel L., Aschemann H., Saurin V., Kostin G.
International Journal of Applied Mathematics and Computer Science
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2016
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tom 26
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nr 1
15-30
EN
In this paper, control-oriented modeling approaches are presented for distributed parameter systems. These systems, which are in the focus of this contribution, are assumed to be described by suitable partial differential equations. They arise naturally during the modeling of dynamic heat transfer processes. The presented approaches aim at developing finitedimensional system descriptions for the design of various open-loop, closed-loop, and optimal control strategies as well as state, disturbance, and parameter estimation techniques. Here, the modeling is based on the method of integrodifferential relations, which can be employed to determine accurate, finite-dimensional sets of state equations by using projection techniques. These lead to a finite element representation of the distributed parameter system. Where applicable, these finite element models are combined with finite volume representations to describe storage variables that are-with good accuracy-homogeneous over sufficiently large space domains. The advantage of this combination is keeping the computational complexity as low as possible. Under these prerequisites, real-time applicable control algorithms are derived and validated via simulation and experiment for a laboratory-scale heat transfer system at the Chair of Mechatronics at the University of Rostock. This benchmark system consists of a metallic rod that is equipped with a finite number of Peltier elements which are used either as distributed control inputs, allowing active cooling and heating, or as spatially distributed disturbance inputs.
6
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Configuring a sensor network for fault detection in distributed parameter systems

75%
Patan M., Uciński D.
International Journal of Applied Mathematics and Computer Science
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2008
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tom 18
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nr 4
513-524
EN
The problem of fault detection in distributed parameter systems (DPSs) is formulated as that of maximizing the power of a parametric hypothesis test which checks whether or not system parameters have nominal values. A computational scheme is provided for the design of a network of observation locations in a spatial domain that are supposed to be used while detecting changes in the underlying parameters of a distributed parameter system. The setting considered relates to a situation where from among a finite set of potential sensor locations only a subset can be selected because of the cost constraints. As a suitable performance measure, the Ds-optimality criterion defined on the Fisher information matrix for the estimated parameters is applied. Then, the solution of a resulting combinatorial problem is determined based on the branch-and-bound method. As its essential part, a relaxed problem is discussed in which the sensor locations are given a priori and the aim is to determine the associated weights, which quantify the contributions of individual gauged sites. The concavity and differentiability properties of the criterion are established and a gradient projection algorithm is proposed to perform the search for the optimal solution. The delineated approach is illustrated by a numerical example on a sensor network design for a two-dimensional convective diffusion process.
7
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Optimal control of nonlinear evolution equations

51%
Papageorgiou N., Yannakakis N.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2001
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tom 21
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nr 1
5-50
EN
In this paper, first we consider parametric control systems driven by nonlinear evolution equations defined on an evolution triple of spaces. The parametres are time-varying probability measures (Young measures) defined on a compact metric space. The appropriate optimization problem is a minimax control problem, in which the system analyst minimizes the maximum cost (risk). Under general hypotheses on the data we establish the existence of optimal controls. Then we pass to nonparametric systems, which are governed by nonlinear evolution equations with nonmonotone operators. We prove two existence results for such evolution inclusions, which are of independent interest and extend significantly the results existing in the literature. Then we solve time-optimal and Meyer-type optimization problems. In Section 5, we derive necessary conditions for saddle point optimality in the minimax control problem. We conclude the paper with three examples of distributed parameter control systems.
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