• Publications
  • Influence
Optimal Control and Applications to Aerospace: Some Results and Challenges
  • E. Trélat
  • Mathematics, Computer Science
  • J. Optim. Theory Appl.
  • 3 April 2012
TLDR
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
Nonlinear Optimal Control via Occupation Measures and LMI-Relaxations
TLDR
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
Global Steady-State Controllability of One-Dimensional Semilinear Heat Equations
TLDR
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
Second order optimality conditions in the smooth case and applications in optimal control
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 theoreticalExpand
Steady-State and Periodic Exponential Turnpike Property for Optimal Control Problems in Hilbert Spaces
TLDR
In this work, we study the steady-state (or periodic) exponential turnpike property of optimal control problems in Hilbert spaces. Expand
Genericity results for singular curves
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 inExpand
Feedback Stabilization of a 1-D Linear Reaction–Diffusion Equation With Delay Boundary Control
  • C. Prieur, E. Trélat
  • Mathematics, Computer Science
  • IEEE Transactions on Automatic Control
  • 7 September 2017
TLDR
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
Uniform controllability of semidiscrete approximations of parabolic control systems
TLDR
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
Optimal Control with State Constraints and the Space Shuttle Re-entry Problem
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 theExpand
GLOBAL STEADY-STATE STABILIZATION AND CONTROLLABILITY OF 1D SEMILINEAR WAVE EQUATIONS
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 byExpand
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