Search results for "principe du maximum"
showing 5 items of 5 documents
Optimal Control of Dissipative Quantum Systems
2008
We study the control of finite dimensional quantum systems by external laser fields. After examining the concrete example of the diatomic molecular alignment in dissipative media, we are interested in the problem of optimal control, where the objective is to bring the system from an initial state into a given final state while minimizing a cost functional. The Pontryagin maximum principle (PMP) provides necessary conditions for optimality, by establishing that any optimal trajectory is the extremal solution of an extended problem of Hamiltonian structure. In this context, we perform the analysis of two particular systems. The first one is a dissipative 2-level system, for which we determine…
Developement of new techniques of Optimal Control in Quantum Dynamics : from nuclear magnetic resonance to molecular physics
2011
The goal of this thesis is to apply the optimal control theory to the dynamics of quantum systems.The first part aim at introducing the tools of optimal control in quantum control which were initially developedin mathematics. This approch has been applied on different kinds of quantum system with small and largedimensions. The first part of this manuscript introduces the optimal control tools which are used with a pointof view suited to a public of physicists. In the second part these techniques are used to control the dynamics ofspins in NMR and MRI. The third part deals with the development of new iterative algorithms applied to thecontrol by laser fields of the rotational dynamics of lin…
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…
Geometry and feedback classification of low-dimensional non-linear control systems
2006
The purpose of this thesis is the study of the local and global differential geometry of fully nonlinear smooth control systems on two-dimensional smooth manifolds. We are particularly interested in the feedback-invariants of such systems. In a first part we will use the Cartan's moving frame method in order to determine these invariants and we will see that one of the most important feedback-invariants is the control analogue to the Gaussian curvature of a surface. As we will explain it, the control curvature reveals very precious information on the optimal synthesis of time optimal problems. In a second part we will construct some microlocal normal forms for time optimal control systems a…
(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 …