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)

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… (More)

We consider the wave and Schrödinger equations on a bounded open connected subset ⌦ of a Riemannian manifold, with Dirichlet, Neumann or Robin boundary conditions whenever its boundary is nonempty.… (More)

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… (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… (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… (More)

Turnpike properties have been established long time ago in finite-dimensional optimal control problems arising in econometry. They refer to the fact that, under quite general assumptions, the optimal… (More)

In this paper, we consider the homogeneous one-dimensional wave equation on [0, π] with Dirichlet boundary conditions, and observe its solutions on a subset ω of [0, π]. Let L ∈ (0, 1). We… (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… (More)