MINES ParisTech CAS - Centre automatique et systèmes

Controllability of some evolution equations by the flatness approach

Authors: Philippe Martin, Lionel Rosier and Pierre Rouchon, Trends in Control and Inverse Problems, 2018, pp. 1-38
The aim of these notes is to introduce the flatness approach for the controllability of PDEs. After discussing the null controllability of the heat equation in dimension one and in dimension N for cylinders, we turn our attention to more general parabolic equation with nonsmooth coefficients. Next we apply the flatness approach to the determination of the reachable states for the heat equation. Finally, we show how to modify the method to deal with the 1D Schro ̈dinger equation. In each situation, the theoretical results are illustrated by numerical simulations. The notes end with some future directions of research.
BibTeX:
@Incollection{,
author = {Philippe Martin, Lionel Rosier and Pierre Rouchon},
title = {Controllability of some evolution equations by the flatness approach},
booktitle = {Trends in Control and Inverse Problems},
editor = {Gerbi, Kaïs Ammari Stéphane},
publisher = {American Institute of Mathematical Sciences},
pages = {1-38},
year = {2018},
abstract = {The aim of these notes is to introduce the flatness approach for the controllability of PDEs. After discussing the null controllability of the heat equation in dimension one and in dimension N for cylinders, we turn our attention to more general parabolic equation with nonsmooth coefficients. Next we apply the flatness approach to the determination of the reachable states for the heat equation. Finally, we show how to modify the method to deal with the 1D Schro ̈dinger equation. In each situation, the theoretical results are illustrated by numerical simulations. The notes end with some future directions of research.}, }

Controllability of Parabolic Equations by the Flatness Approach

Authors: Philippe Martin, Lionel Rosier, Pierre Rouchon, Evolution Equations: Long Time Behavior and Control, pp. 161-178, Cambridge University Press; 2017, DOI: 10.1017/9781108304023.009More...

Feedback Stabilization of Controlled Dynamical Systems

Editor: Nicolas Petit, Vol. 473 in Lecture Notes in Control and Information Sciences, Springer, 2017. ISBN 978-3-319-51297-6.More...

From Pure State and Input Constraints to Mixed Constraints in Nonlinear Systems

Authors: Willem Esterhuizen, Jean Lévine, in Feedback Stabilization of Controlled Dynamical Systems, pp. 125-141, Nicolas Petit Ed., Vol. 473 in Lecture Notes in Control and Information Sciences, Springer-Verlag, March 24 2017. DOI: 10.1007/978-3-319-51298-3_5More...

Asymptotic Expansions of Laplace Integrals for Quantum State Tomography

Authors: Pierre Six, Pierre Rouchon, in Feedback Stabilization of Controlled Dynamical Systems, pp. 307-327, Nicolas Petit Ed., Vol. 473 in Lecture Notes in Control and Information Sciences, Springer-Verlag, March 24 2017. DOI: 10.1007/978-3-319-51298-3_12More...

Estimation of attitude from a single-direction sensor

Authors: L. Magnis, N. Petit, in Multisensor attitude estimation: fundamental concepts and applications, H. Fourati, D. E. C. Belkiat eds., pp. 261-276, CRC Press, 2016More...

Théorie du contrôle: automobile, pétrole, aéronautique

Author: N. Petit, Des mathématiques au monde socio-économique, pp. 17-46, Société Mathématique de France, 2015
Download PDFMore...

Prediction-based control of linear systems by compensating input-dependent input-delay of integral-type

Authors: D. Bresch-Pietri, and N. Petit, in Advances in Delays and Dynamics pp. 79-93, Karafyllis, I., Malisoff, M., Mazenc, F., Pierdomenico, P. eds, Springer 2015
More...

Control-oriented input-delay model of the distributed temperature of a SI engine exhaust catalyst

Authors: D. Bresch-Pietri, T. Leroy, and N. Petit, in Low complexity controllers for time-delay systems, pp. 173-188, C. Bonnet, H. Mounier, H.Özbay and A. Seuret Ed., 2014, Springer
Download PDFMore...

Practical delay modeling of externally recirculated burned gas fraction for Spark-Ignited engines

Authors: D. Bresch-Pietri, T. Leroy, J. Chauvin and N. Petit, Advances in Delays and Dynamics in Delay Systems: from Theory to Numerics and Applications, T. Vyhlídal, J.-F. Lafay, R. Sipahi eds. , pp. 359-372, Springer 2014
Download PDFMore...

Optical-Inertial Tracking System with High Bandwidth and Low Latency

Authors: Göntje C Claasen, Philippe Martin, Frédéric Picard, in Recent Advances in Robotics and Automation, pp 171-181, Springer Berlin Heidelberg, DOI: 10.1007/978-3-642-37387-9_13More...

Control problems for one-dimensional fluids and reactive fluids with moving interfaces

Author: Nicolas Petit, Advances in the Theory of Control, Signals and Systems with Physical Modelling, (eds) J. Lévine and Ph. Müllhaupt, (Lecture Notes In Control and Information Sciences 407), ISBN: 978-3-642-16134-6, pp 323-337, Springer 2010 Download PDFMore...

Flatness Characterization: Two Approaches

Authors: Felix Antritter, Jean Lévine, Advances in the Theory of Control, Signals and Systems with Physical Modeling, pp. 127-139, LECTURE NOTES IN CONTROL AND INFORMATION SCIENCES, Vol 407, 2011 DOI: 10.1007/978-3-642-16135-3_11 Download PDFMore...

Advances in the Theory of Control, Signals and Systems with Physical Modeling

Authors: Jean Lévine, Philippe Müllhaupt, LECTURE NOTES IN CONTROL AND INFORMATION SCIENCES, Vol. 407, 2011, Springer Verlag DOI: 10.1007/978-3-642-16135-3More...

A Flatness-Based Iterative Method for Reference Trajectory Generation in Constrained NMPC

Authors: J. A. De Doná, F. Suryawan, M. M. Seron, J. Lévine, in NONLINEAR MODEL PREDICTIVE CONTROL, pp. 325-333, Lecture Notes in Control and Information Sciences, Springer Verlag, May 18 2009, DOI: 10.1007/978-3-642-01094-1_27 Download PDFMore...

Analysis and Control of Nonlinear Systems A Flatness-based Approach

Author: Jean Lévine Springer Berlin Heidelberg 2009 DOI: 10.1007/978-3-642-00839-9More...

Systèmes dynamiques et commande

Authors: J. Lévine, P. Rouchon. Web pageMore...

Essential and Redundant Internal Models in Nonlinear Output Regulation

Authors: Lorenzo Marconi, Laurent Praly, in Analysis and Design of Nonlinear Control Systems, Alessandro Astolfi, Lorenzo Marconi eds., Springer Verlag, 2008 DOI: 10.1007/978-3-540-74358-3_16More...

Flat systems, equivalence and trajectory generation

Authors: Philippe Martin, Pierre Rouchon, R. M. Murray
Download PDF