Emmanuel Trélat

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We investigate the problem of exact boundary controllability of semilinear onedimensional heat equations. We prove that it is possible to move from any steady-state to any other by means of a boundary control, provided that both are in the same connected component of the set of steady-states. The proof is based on an effective feedback stabilization(More)
We propose a variational method for tomographic reconstruction of blurred and noised binary images based on a penalization process of a minimization problem settled in the space of bounded variation functions. We prove existence and/or uniqueness results and derive an optimality system, both for the minimization problem and its penalized version. Numerical(More)
We investigate variants of Goddard’s problems for nonvertical trajectories. The control is the thrust force, and the objective is to maximize a certain final cost, typically, the final mass. In this article, performing an analysis based on the Pontryagin Maximum Principle, we prove that optimal trajectories may involve singular arcs (along which the norm of(More)
This article surveys the classical techniques of nonlinear optimal control such as the Pontryagin Maximum Principle and the conjugate point theory, and how they can be implemented numerically, with a special focus on applications to aerospace problems. In practice the knowledge resulting from the maximum principle is often insufficient for solving the(More)
We consider the class of nonlinear optimal control problems (OCP) with polynomial data, i.e., the differential equation, state and control constraints and cost are all described by polynomials, and more generally for OCPs with smooth data. In addition, state constraints as well as state and/or action constraints are allowed. We provide a simple hierarchy of(More)
We consider the homogeneous wave equation on a bounded open connected subset Ω of IR. Some initial data being specified, we consider the problem of determining a measurable subset ω of Ω maximizing the L-norm of the restriction of the corresponding solution to ω over a time interval [0, T ], over all possible subsets of Ω having a certain prescribed(More)
The aim of this article is to present algorithms to compute the first conjugate time along a smooth extremal curve, where the trajectory ceases to be optimal. It is based on recent theoretical developments of geometric optimal control, and the article contains a review of second order optimality conditions. The computations are related to a test of(More)
A crucial problem in shape deformation analysis is to determine a deformation of a given shape into another one, which is optimal for a certain cost. It has a number of applications in particular in medical imaging. In this article we provide a new general approach to shape deformation analysis, within the framework of optimal control theory, in which a(More)
Let M be a smooth manifold and Dm, m > 2, be the set of rank m distributions on M endowed with the Whitney C∞ topology. We show the existence of an open set Om dense in Dm, so that, every nontrivial singular curve of a distribution D of Om is of minimal order and of corank one. In particular, for m > 3, every distribution of Om does not admit nontrivial(More)