WorldCat Identities

Caillau, Jean-Baptiste

Overview
Works: 16 works in 25 publications in 2 languages and 138 library holdings
Roles: Editor, Other, Opponent, Thesis advisor, Author
Classifications: TA1637.5, 515.64
Publication Timeline
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Most widely held works by Jean-Baptiste Caillau
Variational methods in imaging and geometric control by Maïtine Bergounioux( )

7 editions published in 2017 in English and held by 120 WorldCat member libraries worldwide

Intro -- Contents -- Part I -- 1 Second-order decomposition model for image processing: numerical experimentation -- 1.1 Introduction -- 1.2 Presentation of the model -- 1.3 Numerical aspects -- 1.3.1 Discretized problem and algorithm -- 1.3.2 Examples -- 1.3.3 Initialization process -- 1.3.4 Convergence -- 1.3.5 Sensitivity with respect to sampling and quantification -- 1.3.6 Sensitivity with respect to parameters -- 1.4 Conclusion -- 2 Optimizing spatial and tonal data for PDE-based inpainting -- 2.1 Introduction -- 2.2 A review of PDE-based image compression -- 2.2.1 Data optimization -- 2.2.2 Finding good inpainting operators -- 2.2.3 Storing the data -- 2.2.4 Feature-based methods -- 2.2.5 Fast algorithms and real-time aspects -- 2.2.6 Hybrid image compression methods -- 2.2.7 Modifications, extensions and applications -- 2.2.8 Relations to other methods -- 2.3 Inpainting with homogeneous diffusion -- 2.4 Optimization strategies in 1D -- 2.4.1 Optimal knots for interpolating convex functions -- 2.4.2 Optimal knots for approximating convex functions -- 2.5 Optimization strategies in 2D -- 2.5.1 Optimizing spatial data -- 2.5.2 Optimizing tonal data -- 2.6 Extensions to other inpainting operators -- 2.6.1 Optimizing spatial data -- 2.6.2 Optimizing tonal data -- 2.7 Summary and conclusions -- 3 Image registration using phase-amplitude separation -- 3.1 Introduction -- 3.1.1 Current literature -- 3.1.2 Our approach -- 3.2 Definition of phase-amplitude components -- 3.2.1 q-Map and amplitude distance -- 3.2.2 Relative phase and image registration -- 3.3 Properties of registration framework -- 3.4 Gradient method for optimization over G -- 3.4.1 Basis on T?id (G) -- 3.4.2 Mean image and group-wise registration -- 3.5 Experiments -- 3.5.1 Pairwise image registration -- 3.5.2 Registering multiple images -- 3.5.3 Image classification
Contrôle optimal géométrique : méthodes homotopiques et applications by Olivier Cots( Book )

2 editions published in 2012 in French and held by 2 WorldCat member libraries worldwide

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 relaxation time. Both sub-systems are driven by the same control. The problem consists in bringing to zero the magnetization of one of the two system while maximizing the magnetization of the second one. This problem comes from constrast imaging in Nuclear Magnetic Resonance and consists in maximising the contrast between two areas of the image. The use of geometrical and numerical tools has given a very precise sub-optimal synthesis for two particular cases (deoxygenated/oxygenated blood and cerebrospinal fluid/water cases). The last contribution of this thesis is about the Lindblad equations in the two-level case. The model is based upon the minimisation of the transfer energy. We restrict the study to a particular case for which the Hamiltonian given by the PMP is Liouville integrable.We describe the conjugate and cut loci for this Riemannian with drift problem
Contribution à l'étude du contrôle en temps minimal des transferts orbitaux by Jean-Baptiste Caillau( Book )

2 editions published in 2000 in French and held by 2 WorldCat member libraries worldwide

Le contexte de ce travail est la mécanique spatiale. Plus précisement, on s'est intéressé, dans le cadre d'une collaboration avec le Centre National d'Études Spatiales, au problème du transfert orbital. Le modèle étudié est celui du contrôle en temps minimal d'un satellite que l'on souhaite insérer sur une orbite géostationnaire. Les contributions de cette thèse sont de trois ordres. Géométrique, tout d'abord, puisqu'on étudie la contrôlabilité du système ainsi que la géométrie des transferts (structure de la commande) à l'aide d'outils de contrôle géométrique. Sont ensuite présentées des méthodes de résolution spectrales et pseudo-spectrales utilisant les polynômes de Tchebycheff, puis des algorithmes basés sur un calcul adaptatif de discrétisation par ondelettes. Ces approches permettent de traiter numériquement le cas d'un satellite dont la poussée est forte à moyenne. Pour atteindre le domaine des poussées faibles, caractéristiques de la future propulsion électro-ionique, il faut finalement introduire de nouvelles techniques qui ont en commun d'être paramétriques (paramétrisation par la poussée ou par le critère). L'analyse des propriétés de ces méthodes se fait naturellement à l'aide de résultats de contrôle paramétrique
Contrôle optimal et métriques de Clairaut-Liouville avec applications by Lionel Jassionnesse( Book )

2 editions published in 2014 in French and held by 2 WorldCat member libraries worldwide

Le travail de cette thèse porte sur l'étude des lieux conjugué et de coupure de métriques riemanniennes ou pseudo-riemanniennes en dimension 2. On se place du point de vue du contrôle optimal pour appliquer le principe du maximum de Pontryagin afin de caractériser les extrémales des problèmes considérés.On va utiliser des méthodes géométriques, numériques et d'intégrabilité pour étudier des métriques de Clairaut-Liouville ou de Liouville sur la sphère. Dans le cas dégénéré de révolution, l'étude de l'ellipsoïde utilise des méthodes géométriques pour déterminer le lieu de coupure et la nature du lieu conjugué dans les cas oblat et prolat. Dans le cas général, les extrémales auront deux types de comportements distincts qui se rapportent à ceux observés dans le cas de révolution, et sont séparés par celles passant par des points ombilicaux. Les méthodes numériques sont utilisées pour retrouver rapidement la dernière conjecture géométrique de Jacobi : le lieu de coupure est un segment et le lieu conjugué contient quatre points de rebroussement.L'étude d'une métrique pseudo-riemannienne vient d'un problème de contrôle quantique où le but est de transférer en temps minimal l'état d'un spin à travers une chaîne de trois spins couplés par des interactions de type Ising. Après réduction, la métrique obtenue possède une intégrale première supplémentaire et on peut donc la mettre sous forme de Liouville, ce qui nous donne les équations des géodésiques. En dehors du cas particulier de Grushin, dont la caustique est décrite, on utilise les méthodes numériques pour étudier le lieu conjugué et le lieu de coupure dans le cas général
Contribution à l'étude du contrôle en temps minimal des transferts orbitaux by Jean-Baptiste Caillau( )

1 edition published in 2005 in French and held by 1 WorldCat member library worldwide

Le contexte de ce travail est la mécanique spatiale. Plus précisement, on s'est intéressé, dans le cadre d'une collaboration avec le Centre National d'Études Spatiales, au problème du transfert orbital. Le modèle étudié est celui du contrôle en temps minimal d'un satellite que l'on souhaite insérer sur une orbite géostationnaire. Les contributions de cette thèse sont de trois ordres. Géométrique, tout d'abord, puisqu'on étudie la contrôlabilité du système ainsi que la géométrie des transferts (structure de la commande) à l'aide d'outils de contrôle géométrique. Sont ensuite présentées des méthodes de résolution spectrales et pseudo-spectrales utilisant les polynômes de Tchebycheff, puis des algorithmes basés sur un calcul adaptatif de discrétisation par ondelettes. Ces approches permettent de traiter numériquement le cas d'un satellite dont la poussée est forte à moyenne. Pour atteindre le domaine des poussées faibles, caractéristiques de la future propulsion électro-ionique, il faut finalement introduire de nouvelles techniques qui ont en commun d'être paramétriques (paramétrisation par la poussée ou par le critère). L'analyse des propriétés de ces méthodes se fait naturellement à l'aide de résultats de contrôle paramétrique
Contribution au contrôle optimal du problème circulaire restreint des trois corps by Bilel Daoud( )

1 edition published in 2011 in French and held by 1 WorldCat member library worldwide

Discrete and continuous dynamical systems : special issue on optimal control and related fields by Jean-Baptiste Caillau( Book )

1 edition published in 2015 in English and held by 1 WorldCat member library worldwide

Optimal control of aerospace systems with control-state constraints and delays by Riccardo Bonalli( )

1 edition published in 2018 in English and held by 1 WorldCat member library worldwide

In this work, we address the real-time optimal guidance of launch vehicles with the objective of designing an autonomous algorithm for the prediction of optimal control strategies, based on indirect methods, able to adapt itself to unpredicted changes of the original scenario. To this aim, we first provide an accurate geometric analysis in the presence of mixed control-state constraints to recover a well-posed framework and correctly apply indirect methods. A practical numerical integration of the problem is proposed by efficiently combining indirect methods with homotopy procedures, increasing robustness and computational speed. Moreover, we improve dynamical models by considering delays. More specifically, we introduce a rigorous and well-posed homotopy framework to recover solutions for optimal control problems with delays via indirect methods. All our contributions made possible the development of a fully automatic, independent and self-regulating software, today property of ONERA-The French Aerospace Lab, for general realistic endo-atmospheric launch vehicle applications focused on optimal missile interception scenarios
Minimisation L¹ en mécanique spatiale by Zheng Chen( )

1 edition published in 2016 in English and held by 1 WorldCat member library worldwide

In astronautics, an important issue is to control the motion of a satellite subject to the gravitation of celestial bodies in such a way that certain performance indices are minimized (or maximized). In the thesis, we are interested in minimizing the L¹-norm of control for the circular restricted three-body problem. The necessary conditions for optimality are derived by using the Pontryagin maximum principle, revealing the existence of bang-bang and singular controls. Singular extremals are analyzed, and the Fuller phenomenon shows up according to the theories developed by Marchal [1] and Zelikin et al. [2, 3]. The controllability for the controlled two-body problem (a degenerate case of the circular restricted three-body problem) with control taking values in a Euclidean ball is addressed first (cf. Chapter 2). The controllability result is readily extended to the three-body problem since the drift vector field of the three-body problem is recurrent. As a result, if the admissible controlled trajectories remain in a fixed compact set, the existence of the solutions of the L¹-minimizaion problem can be obtained by a combination of Filippov theorem (see [4, Chapter 10], e.g.) and a suitable convexification procedure (see, e.g., [5]). In finite dimensions, the L¹-minimization problem is well-known to generate solutions where the control vanishes on some time intervals. While the Pontryagin maximum principle is a powerful tool to identify candidate solutions for L1-minimization problem, it cannot guarantee that the these candidates are at least locally optimal unless sufficient optimality conditions are satisfied. Indeed, it is a prerequisite to establish (as well as to be able to verify) the necessary and sufficient optimality conditions in order to solve the L¹-minimization problem. In this thesis, the crucial idea for establishing such conditions is to construct a parameterized family of extremals such that the reference extremal can be embedded into a field of extremals. Two no-fold conditions for the canonical projection of the parameterized family of extremals are devised. For the scenario of fixed endpoints, these no-fold conditions are sufficient to guarantee that the reference extremal is locally minimizing provided that each switching point is regular (cf. Chapter 3). If the terminal point is not fixed but varies on a smooth submanifold, an extra sufficient condition involving the geometry of the target manifold is established (cf. Chapter 4). Although various numerical methods, including the ones categorized as direct [6, 7], in- direct [5, 8, 9], and hybrid [10], in the literature are able to compute optimal solutions, one cannot expect a satellite steered by the precomputed optimal control (or nominal control) to move on the precomputed optimal trajectory (or nominal trajectory) due to unavoidable perturbations and errors. In order to avoid recomputing a new optimal trajectory once a deviation from the nominal trajectory occurs, the neighboring optimal feedback control, which is probably the most important practical application of optimal control theory [11, Chapter 5], is derived by parameterizing the neighboring extremals around the nominal one (cf. Chapter 5). Since the optimal control function is bang-bang, the neighboring optimal control consists of not only the feedback on thrust direction but also that on switching times. Moreover, a geometric analysis shows that it is impossible to construct the neighboring optimal control once a conjugate point occurs either between or at switching times
Interplanetary transfers with low consumption using the properties of the restricted three body problem by Maxime Chupin( )

1 edition published in 2016 in English and held by 1 WorldCat member library worldwide

The first objective of this work is to understand the dynamical properties of the circular restricted three body problem in order to use them to design low consumption missions for spacecrafts with a low thrust engine. A fundamental property is the existence of invariant manifolds associated with periodic orbits around Lagrange points. Following the Interplanetary Transport Network concept, invariant manifolds are very useful to design spacecraft missions because they are gravitational currents. A large part of this work is devoted to designing a numerical method that performs an optimal transfer between invariant manifolds. The cost we want to minimize is the L1-norm of the control which is equivalent to minimizing the consumption of the engines. We also consider the L2-norm of the control which is easier to minimize numerically. The numerical methods are indirect ones coupled with different continuations on the thrust, on the cost, and on the final state, to provide robustness. These methods are based on the application of the Pontryagin Maximum Principal. The algorithms developed in this work allow for the design of real life missions such as missions between the realms of libration points. The basic idea is to initialize a multiple shooting method with an admissible trajectory that contains controlled parts (local transfers) and uncontrolled parts following the natural dynamics (invariant manifolds). The methods developed here are efficient and fast (less than a few minutes to obtain the whole optimal trajectory). Finally, we develop a hybrid method, with both direct and indirect methods, to adjust the position of the matching points on the invariant manifolds for missions with large energy gaps. The gradient of the value function is given by the values of the costates at the matching points and does not require any additional computation. Hence, the implementation of the gradient descent is easy
Numerical methods for hybrid control and chance-constrained optimization problems by Achille Sassi( )

1 edition published in 2017 in English and held by 1 WorldCat member library worldwide

This thesis is devoted to the analysis of numerical methods in the field of optimal control, and it is composed of two parts. The first part is dedicated to new results on the subject of numerical methods for the optimal control of hybrid systems, controlled by measurable functions and discontinuous jumps in the state variable simultaneously. The second part focuses on a particular application of trajectory optimization problems for space launchers. Here we use some nonlinear optimization methods combined with non-parametric statistics techniques. This kind of problems belongs to the family of stochastic optimization problems and it features the minimization of a cost function in the presence of a constraint which needs to be satisfied within a desired probability threshold
Contrôle optimal et robuste de l'attitude d'un lanceur. Aspects théoriques et numériques by Olivier Antoine( )

1 edition published in 2018 in French and held by 1 WorldCat member library worldwide

L'objectif premier de cette thèse est d'étudier certains aspects du contrôle d'attitude d'un corps rigide, afin d'optimiser la trajectoire d'un lanceur au cours de sa phase balistique. Nous y développons un cadre mathématique permettant de formuler ce problème comme un problème de contrôle optimal avec des contraintes intermédiaires sur l'état. En parallèle de l'étude théorique de ce problème, nous avons mené l'implémentation d'un logiciel d'optimisation basé sur la combinaison d'une méthode directe et d'un algorithme de point intérieur, permettant à l'utilisateur de traiter une phase balistique quelconque. Nous entendons par là qu'il est possible de spécifier un nombre quelconque de contraintes intermédiaires, correspondant à un nombre quelconque de largages de charges utiles. En outre, nous avons appliqué les méthodes dites indirectes, exploitant le principe du maximum de Pontryagin, à la résolution de ce problème de contrôle optimal. On cherche dans ce travail à trouver des trajectoires optimales du point de vue de la consommation en ergols, ce qui correspond à un coût L 1 . Réputé difficile numériquement, ce critère peut être atteint grâce à une méthode de continuation, en se servant d'un coût L 2 comme intermédiaire de calcul et en déformant progressivement ce problème L 2 . Nous verrons également d'autres exemples d'application des méthodes de continuation. Enfin, nous présenterons également un algorithme de contrôle robuste, permettant de rejoindre un état cible à partir d'un état perturbé, en suivant une trajectoire de référence tout en conservant la structure bang-bang des contrôles. La robustesse d'un contrôle peut également être améliorée par l'ajout de variations aiguilles, et un critère qualifiant la robustesse d'une trajectoire à partir des valeurs singulières d'une certaine application entrée-sortie est déduit
Optimisation de consommation pour un véhicule de type voiture by Ouazna Oukacha( )

1 edition published in 2017 in French and held by 1 WorldCat member library worldwide

Cette thèse présente l'étude d'un problème de contrôle optimal dont le coût est non-différentiable pourcertaines valeurs du contrôle ou de l'état, tout en restant Lipschitz. Ce problème nous a été inspiré par laproblématique générale de la minimisation de l'énergie dépensée par un véhicule ou robot de type voiture lelong d'un trajet dont le profil de route est connu à l'avance. Cette problématique est formulée à l'aide d'unmodèle simple de la dynamique longitudinale du véhicule et une fonction coût qui englobe la notiond'efficacité du processus de conversion énergétique. Nous présentons un résultat de régularité des contrôles,valable pour la classe des systèmes non-linéaires, affines dans les contrôles, classe à laquelle appartient notreproblème. Ce résultat nous permet d'exclure les phénomènes de chattering de l'ensemble des solutions. Nousréalisons trois études de cas pour lesquelles les trajectoires optimales sont composées d'arcs bang,d'inactivations, d'arcs singuliers et, dans certains cas, de retours en arrière
Approximation by filtering in optimal control and applications *( )

1 edition published in 2017 in English and held by 1 WorldCat member library worldwide

Abstract: Minimum time control of slow-fast systems is considered. In the case of only one fast angle, averaging techniques are available for such systems. The approach introduced in Dargent (2014) and Bombrun et al. (2013) is recalled, then extended to time-dependent systems by means of a suitable filtering operator. The process relies upon approximating the dynamics by means of sliding windows. The size of these windows is an additional parameter that provides intermediate approximations between averaging over the whole fast angle period and the original dynamics. The motivation is that averaging over an entire period may not provide a good enough approximation to initialize a convergent numerical resolution of the original system; considering a continuous set of intermediate approximations (filtering over windows of size varying from the period to zero) may ensure that convergence. The method is illustrated on problems coming from space mechanics
Contrôlabilité en dimension finie et infinie et applications à des systèmes non linéaires issus du vivant by Clément Moreau( )

1 edition published in 2020 in English and held by 1 WorldCat member library worldwide

This thesis deals with mathematical aspects of controllability of micro-swimming robots and of motility of micro-filaments, with ramifications in control theory and modeling. The first part presents our control theory results. On the one hand, we state a necessary condition of local controllability for a particular class of systems with two controls, based on the study of the Chen-Fliess series associated to these systems. On the other hand, we establish controllability for linear coupled parabolic systems of partial differential equations with nonnegative state constraint. We show that it is possible to control these systems while making sure that the state remains approximately nonnegative when the diffusion matrix is diagonalizable, and that it remains nonnegative in the particular case where it is equal to the identity matrix.The second part addresses applications to micro-swimming, and illustrates the results of the first part. More precisely, we study planar magnetic micro-swimmer robots made of two or three segments, connected by elastic joints, and controlled by a magnetic field. We show that these robots are not controllable in general around their equilibrium position, and describe explicitly the cases for which local controllability can be obtained. The results are illustrated by numerical simulations.In the third part are featured works of modeling and numerical simulation around elastic micro-filaments motility at low Reynolds number. We describe an efficient, robust and versatile N-link model. We numerically validate it by comparing it to another model, and use it to conduct a numerical study of filament buckling
Théorie de contrôle et systèmes dynamiques by Ayadi Lazrag( )

1 edition published in 2014 in English and held by 1 WorldCat member library worldwide

This thesis is devided into three parts. In the first part we begin by describing some well known results in geometric control theory such as the Chow Rashevsky Theorem, the Kalman rank condition, the End-Point Mapping and the linear test. Moreover, we define and study briefly local controllability around a reference control at first and second order. In the second part we provide an elementary proof of the Franks lemma for geodesic flows using basic tools of geometric control theory. In the last part, given a compact Riemannian manifold, we prove a uniform Franks' lemma at second order for geodesic flows and apply the result in persistence theory. In this part we introduce with more details notions of local controllability at first and second order. In fact, we provide a second order controllability result whose proof is long and technical
 
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