1. N. Boizot, E. Busvelle On the stability of a differential Riccati equation for continuous-discrete observers International Journal of Control, 89(2), 322-336, 2016
  2. C.Hermerel,A.Choux,L.Jeannot,E.Busvelle,P.Merillot,and O.Legaie, Characterization of the microshell surface using holography, Fusion Science and Technology, vol. 59, no. 1, p. 110, 2011.
  3. I. Abraham, S. Bruno, O. Durand, P. Gaillard, J. Lagrange, F. Lamy, J. Peyrat, A. Choux, L. Druoton, G. Pascal, E. Busvelle, et al. Experimental measurements and mathematics ; les mesures experimentales et les mathematiques, Chocs, pp. 47–57, 2011.
  4. F. Lafont, E. Busvelle and J.-P. Gauthier, An adaptive high-gain observer for wastewater treatment systems Journal of Process Control, Vol. 21, Issue 6, pp. 893-900, 2011
  5. S.Haan,J.Salmonson,D.Clark,D.Ho,B.Hammel,D.Callahan,C.Cerjan,M.Edwards, S. Hatchett, O. Landen, E. Busvelle, et al. Nif ignition target requirements, margins, and uncertainties : status february 2010 Fusion Science and Technology, vol. 59, no. 1, p. 1, 2011.
  6. N. Boizot, E. Busvelle, J.P. Gauthier, An adaptive high-gain observer for nonlinear systems Automatica, Vol 46, Issue 9, pp. 1483-1488, 2010
  7. A. Choux, L. Jeannot, F. Gillot, F. Sandras, M. Martin, C. Gauvin, G. Pascal, E. Busvelle, J. P. Gauthier, P. Baclet Spatial reconstruction algorithm of Deuterium-Tritium layer in cryogenic targets using optical techniques, Fusion Science and Technology, Volume 51, Number 4, Pages 727-736, May 2007
  8. A. Choux, E. Busvelle, J.-P. Gauthier, G. Pascal Observer for thick layer of solid Deuterium-Tritium using backlit optical shadowgraphy, Applied Optics, Vol. 46, Issue 33, pp. 8193-8201, 2007 PDF
  9. E. Busvelle, J.-P. Gauthier Observation and identification tools for nonlinear systems. Application to a fluid catalytic cracker. Abstract. In this paper, we recall general methodologies we developed for observation and identification in nonlinear systems theory, and we show how they can be applied to real practical problems.
    In a previous paper, we introduced a filter which is intermediate between the extended Kalman filter in its standard version and its high-gain version, and we applied it to certain observation problems. But we were missing some important cases. Here, we show how to treat these cases.
    We also apply the same technique in the context of our identifiability theory.
    As non academic illustrations, we treat a problem of observation and a problem of identification, for a fluid catalytic cracker (FCC). This FCC unit is one of the most crucial from the economic point of view, in petroleum industry.
    International Journal of Control, Vol. 78, 3, 2005 PDF
  10. E. Busvelle, J.-P. Gauthier On determining unknown functions in differential systems, with an application to biological reactors, Abstract. In this paper, we consider general nonlinear systems with observations, containing a (single) unknown function φ We study the possibility to learn about this unknown function via the observations: if it is possible to determine the [values of the] unknown function from any experiment [on the set of states visited during the experiment], and for any arbitrary input function, on any time interval, we say that the system is ''identifiable''.
    For systems without controls, we give a more or less complete picture of what happens for this identifiability property.\ This picture is very similar to the picture of the ''observation theory'' in (1):
    If the number of observations is three or more, then, systems are generically identifiable.
    If the number of observations is 1 or 2, then the situation is reversed. Identifiability is not at all generic. In that case, we add a more tractable infinitesimal condition, to define the ''infinitesimal identifiability'' property.
    This property is so rigid, that we can almost characterize it (we can characterize it by geometric properties, on an open-dense subset of the product of the state space X by the set of values of φ). This, surprisingly, leads to a non trivial classification, and to certain corresponding ''identifiability normal forms''.
    Contrarily to the case of the observability property, in order to identify in practice, there is in general no hope to do something better than using ''approximate differentiators'', as show very elementary examples.
    As an illustration of what may happen in controlled cases, we consider the equations of a biological reactor, (2), (3), in which a population is fed by some substrate. The model heavily depends on a ''growth function'', expressing the way the population grows in presence of the substrate.
    The problem is to identify this ''growth function''. Our result, in the case where the observed variable is the concentration of the substrate, is as follows: the system is identifiable along a trajectory, if and only if this trajectory visits the same value of the output at least twice. We propose also a practical methodology for identification, which shows very reasonable performances.
    (1) J.-P. Gauthier, I. Kupka, Deterministic Observation Theory and Applications, Cambridge University Press, 2001
    (2) G. Bastin, D. Dochain, Adaptive Control of Bioreactors, Elsevier, 1990
    (3) J.-P. Gauthier, H. Hammouri, S. Othman, A simple observer for nonlinear systems, Application to bioreactors, IEEE Trans. On Aut. Control, 37, p875-880, 1992
    COCV, Vol. 9, 2003, p. 509 PDF simulation result
  11. E. Busvelle, J.-P. Gauthier High-Gain and Non-High-Gain Observers for Nonlinear Systems, Abstract. In this paper, following ideas already developped in (1), we construct an observer for nonlinear systems that looks like the extended Kalman filter. In fact, it is asymptotically (in time) exactly the deterministic version of the extended Kalman filter, and when the ''innovation'' is large, it is an high gain observer. In the context of the theory developped in (1), we show that it works for ''all observable systems''. In the paper, we prove convergence of the estimation error, we give several estimates of this error, and we show a convincing illustrative application (a distillation column).
    (1) J.-P. Gauthier, I. Kupka, Deterministic observation theory and applications, Cambridge University Press, 2001.
    in Contemporary Trends in Nonlinear Geometric Control Theory and its Applications, World Scientific, 2002 PDF
  12. B. Bonnard, E. Busvelle, G. Launay Geometric optimal control of the atmospheric arc for a space shuttle, Abstract. We give preliminary remarks concerning the optimal control of the atmospheric arc for a space shuttle (earth re-entry or Mars sample return project). The system governing the trajectories is 6-dimensional, the control is the bank angle, the cost--integrand is the thermal flux and we have state constraints on the thermal flux and the normal acceleration. Our study is geometric and founded on the analysis of the solutions of a minimum principle and direct evaluation of the small--time reachable set for the problem taking into account the state constraints.
    in Contemporary Trends in Nonlinear Geometric Control Theory and its Applications, World Scientific, 2002 PDF
  13. F. Viel, E. Busvelle, J.-P. Gauthier A stable control structure for binary distillation columns Abstract. A Liapunov-based controller for the composition control of binary distillation columns has been developed. It takes into account physical constraints on the inputs and ensures the global asymptotic stability of the closed-loop system with robustness to modelling errors and with the capability of performing set-point tracking and (approximate) disturbance rejection. This controller requires the knowledge of the internal state of the model and this leads to the design of an exponentially converging "high-gain" observer. We arrive at the global asymptotic stability of the whole control structure (the controller + the observer) by proving a somewhat general nonlinear separation principle.
    , Int. J. of Control, Vol 67, No 4, 1997
  14. F. Viel, E. Busvelle, J.-P. Gauthier Stability of a non-linear controller using a high-gain observer for polymerization reactor Abstract. We develop in this paper an observed-based control structure for a standard nonlinear model of polymerization reactors. We use a classical input/output linearization technique for the controller synthesis and prove theoretically its global asymptotic stability. Because our stabilizing feedback laws require the knowledge of the state of the model, we solve the estimation problem by designing an exponentially converging observer, the equations of which are close to those of the extended Kalman filter. Finally, by proving a nonlinear separation principle, we conclude that our observed-based control structure is capable of stabilizing polymerization reactors. As a consequence, polymerization reactors can be operated even on open-loop unstable steady states.
    , Automatica, 31:6, June 1995
  15. E. Busvelle, R. Kharab, A. J. Maciejewski, J.-M. Strelcyn, Numerical Integration of Differential Equations in Presence of First Integrals: Observer Method Abstract. We introduce a simple and powerful procedure - the observer method - in order to obtain a reliable method of numerical integration over an arbitrary long interval of time for systems of ordinary differential equations having first integrals. This aim is achieved by a modification of the original system such that the level manifold of the first integrals becomes a local attractor. We provide the theoretical justification of this procedure. We report many tests and examples dealing with a large spectrum of systems with different dynamical behavior. The comparison with standard and symplectic methods of integration is also provided.
    , Applicationes Mathematicae Vol 22, No 3 1994
  16. F. Viel, E. Busvelle, J.-P. Gauthier A new method for instrument fault detection, Revue européenne diagnostic et sureté de fonctionnement, Vol 4, No 3, ( 1994) Article sélectionné du TOOLDIAG'93, Toulouse, France
  17. F. Deza, E. Busvelle, J.-P. Gauthier, D. Rakotopara Exponential observers for nonlinear systems, IEEE Transactions on Automatic Control Vol 38, No 3, ( 1993)
  18. F. Deza, E. Busvelle, J.-P. Gauthier Exponentially Converging Observers for Distillation Columns and Internal Stability of the Dynamic Output Feedback, Chemical Engineering Science, Vol 47, No 15/16, (1992)
  19. F. Deza, E. Busvelle, J.-P. Gauthier, D. Rakotopara High Gain Estimation for Nonlinear Systems, Systems & Control Letters, 18 (1992)
  20. F. Deza, E. Busvelle, J.-P. Gauthier, D. Rakotopara A stability result on the continuous-continuous and continuous-discret extended Kalman filters, Compte-Rendus de l'Académie des Sciences de Paris, 314, Février 1992

Book's chapter

  1. N. Boizot, E. Busvelle Adaptive-Gain Observers and Applications in "Nonlinear Observers and Applications, Gildas Besançon (Ed), Lecture Notes in Control and In formation Sciences, Vol. 363, Springer, 2007 Material presented at the 28th International Grenoble Summer School in Automatic Control

International conferences

  1. Bouallouche D., Vioix JB., Millot S. and Busvelle E. (2015) Address Matching Using Truck Tours Feedback , Proceedings of the Hamburg International Conference of Logistics (HICL) Vol. 22, 391-418, Hamburg 2015,
  2. Choux, A., Dutto, V., Busvelle, E., Gauthier, JP Study of the phase contrast for the characterization of the surface of Laser Megajoule microshell, World Conference of Non Destructive Testing, Munich, 13-17th June 2016
  3. Gee, C., Gobin, B., Busvelle, E., Villette, S., Jones, G., & Paoli, J. N. I-weed robot: a robot for a specific spraying. In 22e Conférence du COLUMA. Journées Internationales sur la Lutte contre les Mauvaises Herbes, Dijon, France, 10-12 décembre 2013. (pp. 887-893). Association Française de Protection des Plantes (AFPP).
  4. K. Amiour, T. Bakir, and E. Busvelle, Identification de la force contre-électromotrice de moteurs synchrones à aimants permanents, Septième Conférence Internationale Francophone d’Automatique, (Grenoble), CIFA, juillet 2012.
  5. E. Busvelle, N. Boizot Some new results on the solution of continuous-discrete Riccati equations International conference on Mathematical Control Theory and Mechanics, Steklov Mathematical Institute, 2011
  6. K. D. Sebesta, N. Boizot, E. Busvelle, and J. Sachau Using an adaptive high-gain ex- tended kalman filter with a car efficiency model in ASME 2010 Dynamic Systems and Control Conference, pp. 899–906, American Society of Mechanical Engineers, 2010.
  7. Nicolas Boizot, Eric Busvelle, and Jean-Paul Gauthier Adaptive-gain extended kalman filter: Extension to the continuous-discrete case In Proceedings of the 10th European Control Conference (ECC09), 2009
  8. C. Hermerel, A. Choux, E. Busvelle, P. Merillot, L. Jeannot Caractérisation de la surface de microballon par holographie., Dixième colloque international francophone "Méthodes et Techniques Optiques pour l'Industrie", Club CMOI, Reims, France, Novembre 2009
  9. N. Boizot, E. Busvelle, and J-P. Gauthier Adaptive-gain in extended kalman filtering In International conference on Differential equations and Topology, MSU, Moscow, Fed. of Russia, 2008
  10. N. Boizot, E. Busvelle, J. Sachau High-gain observers and Kalman filtering in hard real-time 9th Real-Time Linux Workshop, November 2-4, 2007, Institute for Measurement Technology, Johannes Kepler University of Linz, PDF /PDF
  11. N. Boizot, E. Busvelle, J.-P. Gauthier, J. Sachau Adaptive-gain Extended Kalman Filter: Application to a series connected DC motor Conference on Systems and Control, May 16-18, 2007, Marrakech, Morocco PDF
  12. E. Busvelle, J.-P. Gauthier, S. Binczak, S. Jacquir, Identification of unknown functions in dynamic systems 17th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2006, Kyoto, Japon, pp. 2157-2162, July 2006 PDF
  13. E. Busvelle, J.-P. Gauthier, New results on identifiability of nonlinear systems Abstract. In this paper, we recall definition of identifiability of nonlinear systems. We prove equivalence between identifiability and smooth identifiability. This new result justifies our definition of identifiability.
    In a previous paper, we have established that if the number of observations is three or more, then, systems are generically identifiable, and that if the number of observations is 1 or 2, then the situation is reversed. Identifiability is not at all generic. Also, we have completely classified infinitesimally identifiable systems in the second case, and in particular, we gave normal forms for identifiable systems. Here, we will give similar results in the first case.
    2nd IFAC Symposium on System, Structure and Control Oaxaca, December 8 - 10, 2004 PDF
  14. J.-P. Gauthier, E. Busvelle Identification of nonlinear systems, Diff 2004, Susdal, Russia, 2004
  15. E. Busvelle, J.-P. Gauthier, Identification of unknown functions in biological and petrochemical reactors, Banach Center Research Group, Geometry of Distributions and Control Systems Research group, 10 - 22 May, Warszawa, Poland
  16. E. Busvelle, J.-P. Gauthier, Observation and identification for nonlinear systems, Banach Center Workshop, Geometry in Nonlinear Control, 16--20 June 2003, Bedlewo, Poland, slides (en /fr)
  17. E. Busvelle, J.-P. Gauthier, Observateur grand-gain et observateur de Kalman étendu, CIRO'02, Marrakesh 2002
  18. E. Busvelle, Y. Le Rouzic, D. Bossanne, F. Viel Dynamic Quality Estimators, 4th International Symposium on Analytical Techniques for Industrial Process Control, Anatech 1994, Mandelieu-la-Napoule, France
  19. F. Viel, E. Busvelle, J.-P. Gauthier A new approach for nonlinear state estimation applied to free radical polymerization, Annual AIChE meeting, Miami, USA
  20. E. Busvelle, F. Deza, J.-P. Gauthier A Stability Result for the Extended Kalman Filter. Application to Industrial Processes, SIAM Conference on control and Its Applications, September 1992, Mineapolis, USA
  21. E. Busvelle, F. Deza, F. Mokrani, S. Hapiak Application of a nonlinear observer to a fluid catalytic craker, NOLCOS'92, Juin 1992 Bordeaux, France
  22. E. Busvelle, D. Rakotopara A necessary condition for the existence of finite dimensional filters for discrete-time nonlinear systems, IEEE 29th Conference on Control Applications, Decembre 1990, Honolulu, Hawai
  23. E. Busvelle, D. Rakotopara Immersion in conditionally gaussian systems and finite dimensional filters, IEEE 29th Conference on Control Applications, Decembre 1990, Honolulu, Hawai
  24. D. de Brucq, P. Courtellemont, E. Busvelle Evolution d'état non-linéaire et filtrage approché par maximum d'entropie, GRETSI, Septembre 1991, Juan-les-Pins, France

Seminaries and french conferences

  1. E. Busvelle, J.-P. Gauthier On determining unknown functions in  differential systems, with an application to biological reactors,  Colloque Commande des systèmes non-linéaires, 19-21 Juin 2002, Metz
  2. E. Busvelle Observers and Filippov optimal synthesis. Application to chemical reactor. observers days at IHP, 2-6 Mars 1998, Centre Emile Borel, Paris.
  3. E. Busvelle Sur la convergence de quelques filtres non linéaires, Comptes-rendus des séminaires de Rouen, Avril 1992, Rouen, France
  4. E. Busvelle Méthode particulaire en filtrage non linéaire, Université Sidi Mohamed Ben Abdellah, Septembre 1990, Fès, Maroc
  5. E. Busvelle Immersions conditionnellement gaussiennes, GRECO CNRS, Mai 1990, Paris, France
  6. E. Busvelle Du filtre de Kalman aux filtres finis, Séminaire d'électronique de Rouen, Novembre 1989, Rouen, France
  7. E. Busvelle Immersions et filtres finis, Séminaire de probabilités de St-Flour, Juillet 1989, St-Flour, France
  8. E. Busvelle De l'usage du théorème de Girsanov et de ses applications, Comptes-rendus des séminaires de Rouen, Mars 1989, Rouen, France

Thèses encadrées et co-encadrées

  1. Kenneth D. Sebesta Optimal Observers and Optimal Control: Improving Car Efficiency with Kalman and Pontryagin PhD Université de Bourgogne/Université du Luxembourg, 24 Juin 2010,
  2. Nicolas Boizot Adaptive high-gain extended Kalman filter and applications PhD Université de Bourgogne/Université du Luxembourg, 30 avril 2010
  3. Alexandre Choux Commande optimale d'un système de conformation cryogénique par chauffage infrarouge d'une couche solide d'isotope de l'hydrogène PhD Université de Bourgogne (avec le CEA), 6 décembre 2006
  4. Frédéric Viel Stabilité des systèmes non linéaires contrôlés par retour d'etat estimé. Application aux réacteurs de polymérisation et aux colonnes à distiller. PhD Université de Rouen (avec Shell Recherche S.A.), 1994


  1. E. Busvelle Sur les observateurs des systèmes non-linéaires, Habilitation à Diriger les Recherches, présentée le 29 Juin 2004 à l'Université de Bourgogne, PDF.
  2. E. Busvelle Immersions et filtres de dimension finie; filtrage particulaire Abstract. Cette thèse est consacrée à la recherche de systèmes admettant un filtre de dimension finie. Les outils utilisés sont issus de la théorie des probabilités et de la géométrie différentielle. Il est surtout donné des conditions suffisantes d'existence de filtres finis pour des systèmes non linéaires, condition évidemment très fortes, mais explicites et constructives. Une utilisation simple et originale de l'équation de Zakaï discrète est ensuite présentée, qui permet d'approcher numériquement sa solution pour une très large classe de systèmes. Des simulations de ces différentes approches ont été effectuées et sont présentées à la fin de cette étude.
    Thèse de l'université de Rouen, soutenue en Octobre 1991 PDF,


  1. E. Busvelle + coinventeurs Method for the contactless measurement of three-dimensional objects with two layers by single-view backlit shadowgraphy US-Patent 7,864,339 B2, Jan 4, 2011
    Procédé de mesure sans contact d'objets tridimensionnels à deux couches par ombroscopie optique à une seule vue Titulaire: Commissariat à l'Energie Atomique, Brevet 07802765.3 - 2213 - PCT/EP2007058690, 27 mars 2009