Heating source localization in a reduced time

Beddiaf, Sara; Autrique, Laurent; Perez, Laetitia; Jolly, Jean-Claude

doi:10.1515/amcs-2016-0043

Cited by 6 publications

(3 citation statements)

References 38 publications

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“…This method is based on the Conjugate Gradient Method (CGM) which acts as an iterative regularization method (convergence of this well-known minimization method is discussed for linear systems in [15], [16] and for specific non-linear system in [17], [18]). Examples of numerical implementation for identification purposes in a thermal context are given in [19], [20] or [21]. However, in the works cited above, the authors never broached the question of control.…”

Section: Ihcp Resolutionmentioning

confidence: 99%

Quasi-Online Disturbance Rejection for Nonlinear Parabolic PDE using a Receding Time Horizon Control

Azar¹,

Perez²,

Prieur

et al. 2021

2021 European Control Conference (ECC)

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Null controllability of nonlinear partial differential equation is a very complex challenge. The context underlying this study is to improve the behavior of the plasma in a tokamak reactor in order to lengthen the duration of the nuclear fusion process. Considering the class of a specific parabolic PDE, the well known heat equation is nonlinear if thermal properties are temperature dependent. In such a context a numerical method based on the resolution of inverse heat conduction problem is proposed. It aims to provide identified control laws quasi-online in order to guarantee that the thermal state is kept close to its equilibrium state at zero. The iterative conjugate gradient method is implemented in order to control the temperature in the one-dimensional spatial domain despite several disturbances (time-dependent or thermo-dependent). The proposed strategy is based on successive numerical resolutions of ill-posed inverse problem on receding time horizons which are adapted considering the previous evolution of the system. Numerical results in the investigated configuration highlight that identified control laws are able to reject disturbances and to ensure null controllability.

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Section: Ihcp Resolutionmentioning

confidence: 99%

Quasi-Online Disturbance Rejection for Nonlinear Parabolic PDE using a Receding Time Horizon Control

Azar¹,

Perez²,

Prieur

et al. 2021

2021 European Control Conference (ECC)

Self Cite

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“…Here the response y is defined implicitly as the solution of a partial differential equation (PDE). Specifically, consider the contaminating mobile source identification problem which is of paramount interest in security, environmental and industrial monitoring, or pollution control (Khapalov, 2010;Beddiaf et al, 2016). In a typical scenario, after some chemical contamination has occurred, there is a developing plume of dangerous or toxic material.…”

Section: Simulation Examplementioning

confidence: 99%

Construction of constrained experimental designs on finite spaces for a modified Ek-optimality criterion

Uciński

2020

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A simple computational algorithm is proposed for minimizing sums of largest eigenvalues of the matrix inverse over the set of all convex combinations of a finite number of nonnegative definite matrices subject to additional box constraints on the weights of those combinations. Such problems arise when experimental designs aiming at minimizing sums of largest asymptotic variances of the least-squares estimators are sought and the design region consists of finitely many support points, subject to the additional constraints that the corresponding design weights are to remain within certain limits. The underlying idea is to apply the method of outer approximations for solving the associated convex semi-infinite programming problem, which reduces to solving a sequence of finite min-max problems. A key novelty here is that solutions to the latter are found using generalized simplicial decomposition, which is a recent extension of the classical simplicial decomposition to nondifferentiable optimization. Thereby, the dimensionality of the design problem is drastically reduced. The use of the algorithm is illustrated by an example involving optimal sensor node activation in a large sensor network collecting measurements for parameter estimation of a spatiotemporal process.

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“…To the best of the author's knowledge, the papers that are most closely related to this work are Li et al [2014], Beddiaf et al [2015] and Bernstein and Fernandex-Granda [2017]. All these papers attempt to circumvent the condition number lower bounds by changing the error metric to capture "the recovered solution is geographically close to the true solution", as in this paper.…”

Section: Related Workmentioning

confidence: 99%

Local Differential Privacy for Physical Sensor Data and Sparse Recovery

C.¹,

McMillan²

2017

Preprint

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In this work, we exploit the ill-posedness of linear inverse problems to design algorithms to release differentially private data or measurements of the physical system. We discuss the spectral requirements on a matrix such that only a small amount of noise is needed to achieve privacy and contrast this with the ill-conditionedness. We then instantiate our framework with several diffusion operators and explore recovery via 1 constrained minimisation. Our work indicates that it is possible to produce locally private sensor measurements that both keep the exact locations of the heat sources private and permit recovery of the "general geographic vicinity" of the sources.

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Heating source localization in a reduced time

Cited by 6 publications

References 38 publications

Quasi-Online Disturbance Rejection for Nonlinear Parabolic PDE using a Receding Time Horizon Control

Quasi-Online Disturbance Rejection for Nonlinear Parabolic PDE using a Receding Time Horizon Control

Construction of constrained experimental designs on finite spaces for a modified Ek-optimality criterion

Local Differential Privacy for Physical Sensor Data and Sparse Recovery

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