Olivier Cots

Olivier Cots
Ecole Nationale Supérieure d’Electrotechnique, d’Electronique, d’Informatique, d’Hydraulique et des Télécommunications | INP ENSEEIHT · Département Informatique et mathématiques appliquées

Doctor of Engineering

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36
Publications
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308
Citations

Publications

Publications (36)
Article
Full-text available
Regular control problems in the sense of the Legendre condition are defined, and second-order necessary and sufficient optimality conditions in this class are reviewed. Adding a scalar homotopy parameter, differential path-following is introduced. The previous sufficient conditions ensure the definiteness and regularity of the path. The role of aut...
Article
Full-text available
The objective of this article is to introduce the tools to analyze the contrast imaging problem in Nuclear Magnetic Resonance. Optimal trajectories can be selected among extremal solutions of the Pontryagin Maximum Principle applied to this Mayer type optimal problem. Such trajectories are associated to the question of extremizing the transfer time...
Article
Full-text available
In this article, we study the energy minimization problem of dissipative two-level quantum systems whose dynamics is governed by the Kossakowski–Lindblad equations. In the first part, we classify the extremal curve solutions of the Pontryagin maximum principle. The optimality properties are analyzed using the concept of conjugate points and the Ham...
Article
Full-text available
The Euler−Poinsot rigid body motion is a standard mechanical system and it is a model for left-invariant Riemannian metrics on SO(3). In this article using the Serret−Andoyer variables we parameterize the solutions and compute the Jacobi fields in relation with the conjugate locus evaluation. Moreover, the metric can be restricted to a 2D-surface,...
Article
Full-text available
In this article, the minimum time control problem of an electric vehicle is modeled as a Mayer problem in optimal control, with affine dynamics with respect to the control and with state constraints. The candidates as minimizers are selected among a set of extremals, solutions of a Hamil- tonian system given by the maximum principle. An analysis, w...
Preprint
Full-text available
In this article, based on two case studies, we discuss the role of abnormal geodesics in planar Zermelo navigation problems. Such curves are limit curves of the accessibility set, in the domain where the current is strong. The problem is set in the frame of geometric time optimal control, where the control is the heading angle of the ship and in th...
Article
Full-text available
The first aim of this article is to present the link between the turnpike property and the singular perturbations theory: the first one being a particular case of the second one. Then, thanks to this link, we set up a new framework based on continuation methods for the resolution of singularly perturbed optimal control problems. We consider first t...
Chapter
This paper presents SMITH, the working prototype of a new code which significantly improves the accuracy of thermodynamic diagrams thanks to the highly performant numerical technologies including differential homotopy and automatic differentiation.
Article
Full-text available
In this paper, we consider minimal time problems governed by control-affine-systems in the plane, and we focus on the synthesis problem in presence of a singular locus that involves a saturation point for the singular control. After giving sufficient conditions on the data ensuring occurrence of a prior-saturation point and a switching curve, we sh...
Chapter
Full-text available
In this work we are interested in controlling the displacement of particles in interaction with N point vortices, in a two-dimensional fluid and neglecting the viscous diffusion. We want to drive a passive particle from an initial point to a final point, both given a priori, in a given finite time, the control being due to the possibility of impuls...
Article
Full-text available
Helhmoltz-Kirchhoff equations of motions of vortices of an incompressible fluid in the plane define a dynamics with singularities and this leads to a Zermelo navigation problem describing the ship travel in such a field where the control is the heading angle. Considering one vortex, we define a time minimization problem, geometric frame being the e...
Article
In this paper, we address properties of the minimal time synthesis for control-affine-systems in the plane involving a saturation point for the singular control. First, we provide sufficient conditions on the data ensuring occurence of a prior-saturation point. Then, we show that the bridge (i.e., the optimal bang arc issued from the singular locus...
Preprint
Full-text available
In this paper, we consider minimal time problems governed by control-affine-systems in the plane, and we focus on the synthesis problem in presence of a singular locus that involves a saturation point for the singular control. After giving sufficient conditions on the data ensuring occurence of a prior-saturation point and a switching curve, we sho...
Preprint
Full-text available
Helhmoltz-Kirchhoff equations of motions of vortices of an incompressible fluid in the plane define a dynamics with singularities and this leads to a Zermelo navigation problem describing the ship travel in such a field where the control is the heading angle. Considering one vortex, we define a time minimization problem which can be analyzed with t...
Article
Full-text available
In this article, we analyze the time minimal control for the saturation of a pair of spins of the same species but with inhomogeneities of the applied RF-magnetic field, in relation with the contrast problem in Magnetic Resonance Imaging. We make a complete analysis based on geometric control to classify the optimal syntheses in the single spin cas...
Conference Paper
Full-text available
In this article, the minimum time optimal control problem of an aircraft in its climbing phase is studied. First, a reduction of the initial dynamics into a three dimensional single-input system with a linear dependence with respect to the control is performed. This reduced system is then studied using geometric control techniques. In particular, t...
Preprint
Full-text available
In this article, we are interested in optimal aircraft trajectories in climbing phase. We consider the cost index criterion which is a convex combination of the time-to-climb and the fuel consumption. We assume that the thrust is constant and we control the air slope of the aircraft. This optimization problem is modeled as a Mayer optimal control p...
Preprint
Full-text available
In this article, we analyze the time minimal control for the saturation of a pair of spins of the same species but with inhomogeneities of the applied RF-magnetic field, in relation with the contrast problem in Magnetic Resonance Imaging. We make a complete analysis based on geometric control to classify the optimal syntheses in the single spin cas...
Article
Full-text available
Our aim in this work is to synthesize optimal feeding strategies that maximize, over a time period, the biogas production in a continuously filled bioreactor controlled by its dilution rate. Such an anaerobic process is described by a four-dimensional dynamical system. Instead of modeling the optimization of the biogas production as a Lagrange-type...
Article
Full-text available
In this article, the minimum time and fuel consumption of an aircraft in its climbing phase are studied. The controls are the thrust and the lift coefficient and state constraints are taken into account: air slope and speed limitations. The application of the maximum principle leads to parameterize the optimal control and the multipliers associated...
Article
Full-text available
This article deals with the singularly perturbed aircraft minimum time-to-climb problem. First, we introduce a reduced-order problem with affine dynamics with respect to the control and analyze it with the tools from geometric control: maximum principle combined with second order optimality conditions. Then, we compute candidates as minimizers usin...
Technical Report
Full-text available
In this article, the minimum time control problem of an electric vehicle is modeled as a Mayer problem in optimal control, with affine dynamics with respect to the control and with state constraints. The candidates as minimizers are selected among a set of extremals, solutions of a Hamil-tonian system given by the maximum principle. An analysis, wi...
Technical Report
Full-text available
In this article, the minimum time and fuel consumption of an aircraft in its climbing phase is studied using direct and indirect schemes implemented in the Bocop and HamPath softwares. The controls are the thrust and the lift and state constraints are taken into account: air slope and speed limitations. The indirect method is the numerical implemen...
Technical Report
Full-text available
In this article, the contrast imaging problem by saturation in nuclear magnetic resonance is modeled as a Mayer problem in optimal control. The optimal solution can be found as an extremal solution of the Maximum Principle and analyzed with the recent advanced techniques of geometric optimal control. This leads to a numerical investigation based on...
Article
Full-text available
In this article, the contrast imaging problem in nuclear magnetic resonance is modeled as a Mayer problem in optimal control. The optimal solution can be found as an extremal, solution of the Maximum Principle and analyzed with the techniques of geometric control. This leads to a numerical investigation based on so-called indirect methods using the...
Conference Paper
Full-text available
The Euler-Poinsot rigid body problem is a well known model of left-invariant metrics on SO(3). In the present paper we discuss the properties of two related reduced 2D models: the sub-Riemanian metric of a system of three coupled spins and the Riemannian metric associated to the Euler-Poinsot problem via the Serret-Andoyer reduction.We explicitly c...
Article
Full-text available
We analyze the energy-minimizing problem for a two-level dissipative quantum system described by the Kossakowsky-Lindblad equation. According to the Pontryagin maximum principle (PMP), minimizers can be selected among normal and abnormal extremals whose dynamics are classified according to the values of the dissipation parameters. Our aim is to imp...
Conference Paper
Full-text available
In this article, the contrast imaging problem in nuclear magnetic resonance is modeled as a Mayer problem in optimal control. A first synthesis of locally optimal solutions is given in the single-input case using geometric methods based on Pontryagin's maximum principle. We then compare these results using direct methods and a moment-based approach...
Article
Full-text available
The purpose of this paper is to present numerical methods and results about the contrast imaging problem in nuclear magnetic resonance which corresponds to a Mayer problem in optimal control. The candidates as minimizers are selected among a set of extremals, solutions of a Hamiltonian system given by the Pontryagin Maximum Principle and sufficient...
Article
Full-text available
The Euler-Poinsot rigid body motion is a standard mechanical system and is the model for left-invariant Riemannian metrics on SO (3). In this article, using the Serret-Andoyer variables we parameterize the solutions and compute the Jacobi fields in relation with the conjugate locus evaluation. Moreover the metric can be restricted to a 2D surface a...
Thesis
Full-text available
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 o...
Conference Paper
Full-text available
We combine geometric and numerical techniques – the Hampath code – to compute conjugate and cut loci on Riemannian surfaces using three test bed examples: ellipsoids of revolution, general ellipsoids, and metrics with singularities on S 2 associated to spin dynamics.
Presentation
It is well known that solving optimal control problem is difficult by indi- rect methods, because the shooting function is very sensitive with respect to the initial point. An other reason is that, in some case, the Boundary Value Problem we obtain from the application of Pontryagin maximum principle is discontinuous. To deal with these difficultie...
Conference Paper
Full-text available
The aim of this contribution is to refine some of the computations of [6]. The Lindblad equation modelling a two-level dissipative quantum system is investigated. The control can be interpretated as the action of a laser to rotate a molecule in gas phase, or as the effect of a magnetic field on a spin 1/2 particle. For the energy cost, normal extre...

Projects

Projects (3)
Project
Geometry study of Zermelo navigation problem from optimal control point of view