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Your search keyword '"Trelat, Emmanuel"' showing total 25 results
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25 results on '"Trelat, Emmanuel"'

1. Internal Controls for Stochastic Lattice Dynamics

Author

Hannani, Amirali, Phung, Minh-Nhat, Tran, Minh-Binh, and Trélat, Emmanuel

Subjects
Mathematics - Optimization and Control
Abstract

In [6], we have designed impulsive and feed-back controls for harmonic chains with a point thermostat. In this work, a new type of control is proposed: internal control. We study the internal control for for stochastic lattice dynamics, with the goal of controlling the transition kernel of the kinetic equation in the limit., Comment: 38 pages, 1 figure

Published
2024

2. Weyl formulae for some singular metrics with application to acoustic modes in gas giants

Author

de Verdìère, Yves Colin, Dietze, Charlotte, de Hoop, Maarten V., and Trélat, Emmanuel

Subjects
Mathematics - Analysis of PDEs, Astrophysics - Earth and Planetary Astrophysics, Mathematical Physics, Mathematics - Spectral Theory
Abstract

This paper is motivated by recent works on inverse problems for acoustic wave propagation in the interior of gas giant planets. In such planets, the speed of sound is isotropic and tends to zero at the surface. Geometrically, this corresponds to a Riemannian manifold with boundary whose metric blows up near the boundary. Here, the spectral analysis of the corresponding Laplace-Beltrami operator is presented and the Weyl law is derived. The involved exponents depend on the Hausdorff dimension which, in the supercritical case, is larger than the topological dimension.

Published
2024

3. Constructive reachability for linear control problems under conic constraints

Author

Pouchol, Camille, Trélat, Emmanuel, and Zhang, Christophe

Subjects
Mathematics - Optimization and Control
Abstract

Motivated by applications requiring sparse or nonnegative controls, we investigate reachability properties of linear infinite-dimensional control problems under conic constraints. Relaxing the problem to convex constraints if the initial cone is not already convex, we provide a constructive approach based on minimising a properly defined dual functional, which covers both the approximate and exact reachability problems. Our main results heavily rely on convex analysis, Fenchel duality and the Fenchel-Rockafellar theorem. As a byproduct, we uncover new sufficient conditions for approximate and exact reachability under convex conic constraints. We also prove that these conditions are in fact necessary. When the constraints are nonconvex, our method leads to sufficient conditions ensuring that the constructed controls fulfill the original constraints, which is in the flavour of bang-bang type properties. We show that our approach encompasses and generalises several works, and we obtain new results for different types of conic constraints and control systems.

Published
2024

4. Large-time optimal observation domain for linear parabolic systems

Author

Mazari-Fouquer, Idriss, Privat, Yannick, and Trélat, Emmanuel

Subjects
Mathematics - Analysis of PDEs, Mathematics - Optimization and Control
Abstract

Given a well-posed linear evolution system settled on a domain $\Omega$ of $\mathbb{R}^d$, an observation subset $\omega\subset\Omega$ and a time horizon $T$, the observability constant is defined as the largest possible nonnegative constant such that the observability inequality holds for the pair $(\omega,T)$. In this article we investigate the large-time behavior of the observation domain that maximizes the observability constant over all possible measurable subsets of a given Lebesgue measure. We prove that it converges exponentially, as the time horizon goes to infinity, to a limit set that we characterize. The mathematical technique is new and relies on a quantitative version of the bathtub principle.

Published
2024

5. The exponential turnpike property for periodic linear quadratic optimal control problems in infinite dimension

Author

Trélat, Emmanuel, Zeng, Xingwu, and Zhang, Can

Subjects
Mathematics - Optimization and Control
Abstract

In this paper, we establish an exponential periodic turnpike property for linear quadratic optimal control problems governed by periodic systems in infinite dimension. We show that the optimal trajectory converges exponentially to a periodic orbit when the time horizon tends to infinity. Similar results are obtained for the optimal control and adjoint state. Our proof is based on the large time behavior of solutions of operator differential Riccati equations with periodic coefficients.

Published
2024

6. Controlling the Rates of a Chain of Harmonic Oscillators with a Point Langevin Thermostat

Author

Hannani, Amirali, Tran, Minh-Binh, Phung, Minh Nhat, and Trélat, Emmanuel

Subjects
Mathematics - Optimization and Control
Abstract

We consider the control problem for an infinite chain of coupled harmonic oscillators with a Langevin thermostat at the origin. We study the effect of two types of open-loop boundary controls, impulsive control and linear memory-feedback control, in the high frequency limit. We investigate their action on the reflection-transmission coefficients for the wave energy for the scattering of the thermostat. Our study shows that impulsive boundary controls have no impact on the rates and are thus not appropriate to act on the system, despite their physical meaning and relevance. In contrast, the second kind of control that we propose, which is less standard and uses the past of the state solution of the system, is adequate and relevant. We prove that any triple of rates satisfying appropriate assumptions is asymptotically reachable thanks to linear memory-feedback controls that we design explicitly.

Published
2024

7. Linear Control Systems in Banach Spaces

Author

Trélat, Emmanuel, Zuazua, Enrique, Editor-in-Chief, Fonseca, Irene, Series Editor, Hoffmann, Franca, Series Editor, Jin, Shi, Series Editor, Manfredi, Juan J., Series Editor, Trélat, Emmanuel, Series Editor, and Zhang, Xu, Series Editor

Published
2024
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8. Semigroup Theory

Author

Trélat, Emmanuel, Zuazua, Enrique, Editor-in-Chief, Fonseca, Irene, Series Editor, Hoffmann, Franca, Series Editor, Jin, Shi, Series Editor, Manfredi, Juan J., Series Editor, Trélat, Emmanuel, Series Editor, and Zhang, Xu, Series Editor

Published
2024
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9. Optimal Control

Author

Trélat, Emmanuel, Zuazua, Enrique, Editor-in-Chief, Fonseca, Irene, Series Editor, Hoffmann, Franca, Series Editor, Jin, Shi, Series Editor, Manfredi, Juan J., Series Editor, Trélat, Emmanuel, Series Editor, and Zhang, Xu, Series Editor

Published
2024
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10. Stabilization

Author

Trélat, Emmanuel, Zuazua, Enrique, Editor-in-Chief, Fonseca, Irene, Series Editor, Hoffmann, Franca, Series Editor, Jin, Shi, Series Editor, Manfredi, Juan J., Series Editor, Trélat, Emmanuel, Series Editor, and Zhang, Xu, Series Editor

Published
2024
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11. Controllability

Author

Trélat, Emmanuel, Zuazua, Enrique, Editor-in-Chief, Fonseca, Irene, Series Editor, Hoffmann, Franca, Series Editor, Jin, Shi, Series Editor, Manfredi, Juan J., Series Editor, Trélat, Emmanuel, Series Editor, and Zhang, Xu, Series Editor

Published
2024
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13. Convergence in Nonlinear Optimal Sampled-Data Control Problems

Author

Bourdin, Loic and Trelat, Emmanuel

Abstract

Consider, on the one part, a general nonlinear finite-dimensional optimal control problem and assume that it has a unique solution $x^*$. On the other part, consider the sampled-data control version of it. Under appropriate assumptions, we prove that the optimal state of the sampled-data problem converges uniformly to $x^*$ as the norm of the partition tends to zero. Moreover, applying the Pontryagin maximum principle (PMP) to both problems, we prove that, if $x^*$ has a unique weak extremal lift with a costate $p$ that is normal, then the costate of the sampled-data problem converges uniformly to $p$. In other words, under a normality assumption, control sampling commutes, at the limit of small partitions, with the application of the PMP.

Published
2024
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14. Practical and Numerical Considerations

Author

Cunniffe, Nik, Hamelin, Frédéric, Iggidr, Abderrahman, Rapaport, Alain, Sallet, Gauthier, Zuazua, Enrique, Editor-in-Chief, Fonseca, Irene, Series Editor, Hoffmann, Franca, Series Editor, Jin, Shi, Series Editor, Manfredi, Juan J., Series Editor, Trélat, Emmanuel, Series Editor, Zhang, Xu, Series Editor, Cunniffe, Nik, Hamelin, Frédéric, Iggidr, Abderrahman, Rapaport, Alain, and Sallet, Gauthier

Published
2024
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15. Observers Synthesis

Author

Cunniffe, Nik, Hamelin, Frédéric, Iggidr, Abderrahman, Rapaport, Alain, Sallet, Gauthier, Zuazua, Enrique, Editor-in-Chief, Fonseca, Irene, Series Editor, Hoffmann, Franca, Series Editor, Jin, Shi, Series Editor, Manfredi, Juan J., Series Editor, Trélat, Emmanuel, Series Editor, Zhang, Xu, Series Editor, Cunniffe, Nik, Hamelin, Frédéric, Iggidr, Abderrahman, Rapaport, Alain, and Sallet, Gauthier

Published
2024
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16. Introduction

Author

Cunniffe, Nik, Hamelin, Frédéric, Iggidr, Abderrahman, Rapaport, Alain, Sallet, Gauthier, Zuazua, Enrique, Editor-in-Chief, Fonseca, Irene, Series Editor, Hoffmann, Franca, Series Editor, Jin, Shi, Series Editor, Manfredi, Juan J., Series Editor, Trélat, Emmanuel, Series Editor, Zhang, Xu, Series Editor, Cunniffe, Nik, Hamelin, Frédéric, Iggidr, Abderrahman, Rapaport, Alain, and Sallet, Gauthier

Published
2024
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17. Mathematical Foundations

Author

Cunniffe, Nik, Hamelin, Frédéric, Iggidr, Abderrahman, Rapaport, Alain, Sallet, Gauthier, Zuazua, Enrique, Editor-in-Chief, Fonseca, Irene, Series Editor, Hoffmann, Franca, Series Editor, Jin, Shi, Series Editor, Manfredi, Juan J., Series Editor, Trélat, Emmanuel, Series Editor, Zhang, Xu, Series Editor, Cunniffe, Nik, Hamelin, Frédéric, Iggidr, Abderrahman, Rapaport, Alain, and Sallet, Gauthier

Published
2024
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18. Analysis of the Kermack-McKendrick Model

Author

Cunniffe, Nik, Hamelin, Frédéric, Iggidr, Abderrahman, Rapaport, Alain, Sallet, Gauthier, Zuazua, Enrique, Editor-in-Chief, Fonseca, Irene, Series Editor, Hoffmann, Franca, Series Editor, Jin, Shi, Series Editor, Manfredi, Juan J., Series Editor, Trélat, Emmanuel, Series Editor, Zhang, Xu, Series Editor, Cunniffe, Nik, Hamelin, Frédéric, Iggidr, Abderrahman, Rapaport, Alain, and Sallet, Gauthier

Published
2024
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19. Stochastic Tug-of-War Games

Author

Parviainen, Mikko, Zuazua, Enrique, Editor-in-Chief, Fonseca, Irene, Series Editor, Hoffmann, Franca, Series Editor, Jin, Shi, Series Editor, Manfredi, Juan J., Series Editor, Trélat, Emmanuel, Series Editor, Zhang, Xu, Series Editor, and Parviainen, Mikko

Published
2024
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21. Further Regularity Methods

Author

Parviainen, Mikko, Zuazua, Enrique, Editor-in-Chief, Fonseca, Irene, Series Editor, Hoffmann, Franca, Series Editor, Jin, Shi, Series Editor, Manfredi, Juan J., Series Editor, Trélat, Emmanuel, Series Editor, Zhang, Xu, Series Editor, and Parviainen, Mikko

Published
2024
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22. Introduction

Author

Parviainen, Mikko, Zuazua, Enrique, Editor-in-Chief, Fonseca, Irene, Series Editor, Hoffmann, Franca, Series Editor, Jin, Shi, Series Editor, Manfredi, Juan J., Series Editor, Trélat, Emmanuel, Series Editor, Zhang, Xu, Series Editor, and Parviainen, Mikko

Published
2024
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23. Mean Value Characterizations

Author

Parviainen, Mikko, Zuazua, Enrique, Editor-in-Chief, Fonseca, Irene, Series Editor, Hoffmann, Franca, Series Editor, Jin, Shi, Series Editor, Manfredi, Juan J., Series Editor, Trélat, Emmanuel, Series Editor, Zhang, Xu, Series Editor, and Parviainen, Mikko

Published
2024
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24. Viscosity Solutions

Author

Parviainen, Mikko, Zuazua, Enrique, Editor-in-Chief, Fonseca, Irene, Series Editor, Hoffmann, Franca, Series Editor, Jin, Shi, Series Editor, Manfredi, Juan J., Series Editor, Trélat, Emmanuel, Series Editor, Zhang, Xu, Series Editor, and Parviainen, Mikko

Published
2024
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25. Open Problems and Comments

Author

Parviainen, Mikko, Zuazua, Enrique, Editor-in-Chief, Fonseca, Irene, Series Editor, Hoffmann, Franca, Series Editor, Jin, Shi, Series Editor, Manfredi, Juan J., Series Editor, Trélat, Emmanuel, Series Editor, Zhang, Xu, Series Editor, and Parviainen, Mikko

Published
2024
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