Search results for "Optimal control"
showing 10 items of 209 documents
Algebraic-geometric techniques for the feedback classification and robustness of the optimal control of a pair of Bloch equations with application to…
2017
The aim of this article is to classify the singular trajectories associated with the optimal control problems of a pair of controlled Bloch equations. The motivation is to analyze the robustness of the optimal solutions to the contrast and the time-minimal saturation problem, in magnetic resonance imaging, with respect to the parameters and B1-inhomogeneity. For this purpose, we use various computer algebra algorithms and methods to study solutions of polynomial systems of equations and inequalities which are used for classification issues: Gröbner basis, cylindrical algebraic decomposition of semi-algebraic sets, Thom's isotopy lemma.
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…
The Influence of the feedback control of the hexapod platform of the SAAM dynamic driving simulator on neuromuscular dynamics of the drivers
2012
Multi sensorial cues (visual, auditory, haptic, inertial, vestibular, neuromuscular) [Ang2] play important roles to represent a proper sensation (objectively) and so a perception (subjectively as cognition) in driving simulators. Driving simulator aims at giving the sensation of driving as in a real case. For a similar situation, the driver has to react in the same way as in reality in terms of ‘self motion’. To enable this behavior, the driving simulator must enhance the virtual immersion of the subject in the driving situation. The subject has to perceive the motion of his own body in the virtual scene of the virtual car as he will have in a real car. For that reason, restituting the iner…
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…
Optimal Robust Quantum Control by Inverse Geometric Optimization
2020
International audience; We develop an inverse geometric optimization technique that allows the derivation of optimal and robust exact solutions of low-dimension quantum control problems driven by external fields: we determine in the dynamical variable space optimal trajectories constrained to robust solutions by Euler-Lagrange optimization; the control fields are then derived from the obtained robust geodesics and the inverted dynamical equations. We apply this method, referred to as robust inverse optimization (RIO), to design optimal control fields producing a complete or half population transfer and a NOT quantum gate robust with respect to the pulse inhomogeneities. The method is versat…
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…