Search results for "contrôle optimal"
showing 10 items of 20 documents
Optimal control of spin-systems: Applications to Nuclear Magnetic Resonance and Quantum Information
2016
The goal of this thesis is to apply the optimal control theory to Nuclear Magnetic Resonance and Quantum Information. In a first step, we introduce the different topics and the dynamics of the analyzed systems. We give the necessary tools to use the Pontryagin Maximum Principle, and also an optimization algorithm, namely GRAPE. The first work is an application of the PMP to the control of a three-spin chain with unequal couplings. We continue with the study of a classical problem called "the tennis racket effect", which is a non-linear phenomenon occuring during the free rotation of a three-dimensional rigid body. We use the results in the following chapter to determine some control laws fo…
Optimal control and shortcuts to adiabaticity techniques in linear and non-linear systems : from ion cyclotron resonance to nuclear magnetic resonance
2021
The goal of our research is to develop efficient and robust control protocols for classical and quantum systems. To this end, we have applied optimal control theory (OCT) and shortcuts to adiabaticity (STA) with inverse engineering and motion planning approaches in three different examples, which are RC (Resistor Capacitor) circuits, Fourier Transform-Ion Cyclotron Resonance (FT-ICR), and Nuclear Magnetic Resonance (NMR). Some of our results are not limited to these systems but are rather general. We apply OCT and STA with an inverse engineering approach to control the time-evolution of the charge on a capacitor. We show that OCT is a member of the family of STA solutions. In order to contr…
Sur le rôle des singularités hamiltoniennes dans les systèmes contrôlés : applications en mécanique quantique et en optique non-linéaire.
2012
This thesis has two goals: the first one is to improve the control techniques in quantum mechanics, and more specifically in NMR, by using the tools of geometric optimal control. The second one is the study of the influence of Hamiltonian singularities in controlled systems. The chapter about optimal control study three classical problems of NMR : the inversion problem, the influence of the radiation damping term, and the steady state technique. Then, we apply the geometric optimal control to the problem of the population transfert in a three levels quantum system to recover the STIRAP scheme.The two next chapters study Hamiltonian singularities. We show that they allow to control the polar…
Contrôle quantique optimal et robuste dans des systèmes de petite dimension
2020
Optimal control theory (OCT) is the basic and comprehensive method to obtain the optimal solutions of quantum systems controlled by external fields. It provides a powerful set of tools and concepts. One of the goals of the thesis is to design the technique of OCT in two- and three-state quantum systems taking into account losses and robustness, which is of primary importance for the implementation of control techniques in a broad class of platforms.Based on inverse-engineering techniques and the Pontryagin maximum principle (PMP), we establish and test the different optimal strategies showing how to control the transfer in three-level quantum systems considering energy- and time-minimum opt…
Qauntum control of molecular rotation and of processes in Nuclear Magnetic Resonance
2019
The goal of this thesis is to apply quantum control techniques to manipulate molecular rotation and to enhance the efficiency of processes in Nuclear Magnetic Resonance.These techniques have been used theoretically and experimentally to control the orientation of a symmetric top molecule by means of THz laser fields. This study has been extended to the case of a long interaction distance between the field and the sample. In this case, the molecule cannot be approximated as isolated. We have also shown the extend to which the time evolution of the degree of orientation can be shaped. Optimal control techniques were used to design the THz field which allows to reach the corresponding dynamics…
Optimal control of inhomogeneous spin ensembles : applications in NMR and quantum optics
2018
The goal of this thesis is to apply optimal control theory to the dynamics ofinhomogeneous spin ensembles. The first part focuses on the control of a spin ensemble coupled to a cavity. The theory is introduced in detail, and a general method to efficiently control spins ispresented. Several pulses are derived in the bad/good cavity regimes using numerical optimal control techniques. Additionally, non-linear generalized functions are used in order to derivesimple approximated solutions. In a second step, the problem of spin echo Signal to Noise Ratio maximization is investigated, and maximization conditions are derived. It is shown that new pulses are superior to state-of-the-art square puls…
Observateur et contrôle optimal : améliorer l'efficacité de la conduite automobile avec Kalman et Pontryagin
2010
The PhD presents a combined approach to improving individual car efficiency. An optimal observer, the Extended Kalman Filter, is used to create an efficiency model for the car. Particular attention was paid to handling the asynchronous and redundant nature of the measurement data. A low-cost sensor suite developed to measure data is described. This sensor suite was installed on multiple vehicles to good success. It employsan accelerometer, gps, fuel injector timer, and Vss input to measure all the data necessary to reconstruct the car's state. This observer and sensor suite can be used as the base for any study which requires car efficiency maps, allowing research to proceed without manufac…
Optimal control and applications to orbital transfer and almost-riemannian geometry
2010
In this thesis we focus on optimal control techniques as well as geometric control techniques applied to the orbital transfer problem and to almost-Riemannian geometry. In these cases, Pontryagin’s Maximum Principle allows to analyse the extremal flow of affine control systems.In the case of a satellite with low-thrust propulsion, averaging techniques give an approximated system. Averaging is explicit in the energy minimization case and is directly related to almost-riemannian problems. The geometric analysis of such problems is generalized by the study of metrics on the two-sphere of revolution. In this way it is possible to classify the situations considering the transcendance of the solu…
Geometric optimal control : homotopic methods and applications
2012
This work is about geometric optimal control applied to celestial and quantum mechanics. We first dealt with the minimum fuel consumption problem of transfering a satellite around the Earth. This brought to the creation of the code HamPath which permits first of all to solve optimal control problem for which the command law is smooth. It is based on the Pontryagin Maximum Principle (PMP) and on the notion of conjugate point. This program combines shooting method, differential homotopic methods and tools to compute second order optimality conditions. Then we are interested in quantum control. We study first a system which consists in two different particles of spin 1/2 having two different r…
(No title)
2003
The aim of this work is to study multiobjective optimization problems with or without dynamics and the generalized Bolza problem and its applications. After having pointed out some concepts of nonsmooth analysis, we begin the first part of this thesis with the existence of Lagrange multipliers for multiobjective optimization problems in infinite dimension with a general preference. We introduce the regularity of preference and use calmness qualification condition we establish the existence of Karush-Kuhn-Tucker multipliers. This allows us to obtain Fritz-John multipliers in terms of the approximate subdifferential by Ioffe. Then we derive similar results when the preference is defined by a …