This article surveys the usual 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.Expand

We provide a simple hierarchy of LMI- (linear matrix inequality)-relaxations whose optimal values form a nondecreasing sequence of lower bounds on the optimal value of OCPs with polynomial data.Expand

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.Expand

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… Expand

Let $M$ be a smooth manifold and ${\cal D}_m$, $m\geq 2$, be the set of rank $m$ distributions on $M$ endowed with the Whitney $C^\infty$ topology. We show the existence of an open set $O_m$ dense in… Expand

The goal of this paper is to design a stabilizing feedback boundary control for a reaction–diffusion partial differential equation (PDE), where the boundary control is subject to constant delay while the equation may be unstable without any control.Expand

In the present paper, under the main assumptions that the discretized semigroup is uniformly analytic, and that the control operator is mildly unbounded, we prove that the semidiscrete approximation models are uniformly controllable.Expand

In this article, we initialize the analysis under generic assumptions of the small time optimal synthesis for single input systems with state constraints. We use geometric methods to evaluate the… Expand

This paper is concerned with the exact boundary controllability of semilinear wave equations in one space dimension. We prove that it is possible to move from any steady-state to any other one by… Expand