Emmanuel Chambon

Emmanuel Chambon

PhD, Flight Control Engineer, Sailor

Journals

2017

Détermination de matrice semblable Metzler par optimisation non lisse

Emmanuel Chambon, Laurent Burlion, Pierre Apkarian

In Journal Européen des Systèmes Automatisés, 50(1), pp. 75-94, 2017

AbstractShow/Hide BibTeXView onlinejesa_matlab.zip

Abstract

La conception d'observateurs par intervalles repose sur la coopérativité de la dynamique de l'erreur d'observation. La littérature propose un certain nombre de méthodes pour concevoir des observateurs par intervalles sur des systèmes non coopératifs. Ces méthodes sont basées sur des changements de variables, la dynamique de l'erreur d'observation devenant coopérative dans les nouvelles coordonnées. Dans cet article, une méthode permettant la détermination numérique de cette transformation sans hypothèse préalable est introduite. Elle repose sur la reformulation du problème mathématique de détermination du changement de coordonnées adéquat en problème de stabilisation d'un ensemble de modèles dynamiques linéaires. Le problème équivalent est alors résolu en faisant appel à une technique d'optimisation non lisse. L'approche est testée sur deux exemples extraits de la littérature.

@article{chambon_jesa_2016,

title = {D\'{e}termination de matrice semblable Metzler par optimisation non lisse},
journal = {Journal Europ\'{e}en des Syst\`{e}mes Automatis\'{e}s},
author = {Chambon, E. and Burlion, L. and Apkarian, P.},
volume = {50},
number = {1},
pages = {75-94},
month = feb,
year = {2017},
url = {http://emmanuel-chambon.fr/assets/publis/JESA_Chambon_2016.pdf}

}

Time-response shaping using Output to Input Saturation Transformation

Emmanuel Chambon, Laurent Burlion, Pierre Apkarian

In International Journal of Control, pp. 1-20, 2017

AbstractShow/Hide BibTeXView online

Abstract

For linear systems, the control law design is often performed so that the resulting closed-loop meets specific frequency-domain requirements. However, in many cases, it may be observed that the obtained controller does not enforce time-domain requirements amongst which the objective of keeping an output variable in a given interval. In this article, a transformation is proposed to convert prescribed bounds on an output variable into time-varying saturations on the synthesized linear control law. This transformation uses some well-chosen time-varying coefficients so that the resulting time-varying saturations do not overlap in the presence of disturbances. Using an anti-windup approach, it is obtained that the origin of the resulting closed-loop is globally asymptotically stable and that the regulated variable satisfies the time-domain constraints in the presence of an unknown finite-energy bounded disturbance. An application to a linear ball and beam model is presented.

@article{chambon_outputj_2015,

title = {Time-response shaping using Output to Input Saturation Transformation},
journal = {International Journal of Control},
author = {Chambon, E. and Burlion, L. and Apkarian, P.},
pages = {1-20},
month = jan,
year = {2017},
url = {http://emmanuel-chambon.fr/assets/publis/IJC_Chambon_2015.pdf}

}

2016

Overview of linear time-invariant interval observer design: towards a non-smooth optimisation-based approach

Emmanuel Chambon, Laurent Burlion, Pierre Apkarian

In IET Control Theory and Applications, 10(11), pp. 1258-1268, 2016

AbstractShow/Hide BibTeXView online

Abstract

Some applications in control require the state vector of a system to be expressed in the appropriate coordinates so as to satisfy to some mathematical properties which constrain the studied system dynamics. This is the case with the theory of linear interval observers which are trivial to implement on cooperative systems, a rather limited class of control systems. The available literature shows how to enforce this limiting cooperativity condition for any considered system through a state-coordinate transformation. This article proposes an overview of the existing numerical techniques to determine such a transformation. It is shown that in spite of being practical, these techniques have some limitations. Consequently, a reformulation of the problem is proposed so as to apply non-smooth control design techniques. A solution is obtained in both the continuous- and discrete-time frameworks. Interestingly, the new method allows to formulate additional control constraints. Simulations are performed on three examples.

@article{chambon_iet_2016,

title = {Overview of linear time-invariant interval observer design: towards a non-smooth optimisation-based approach},
journal = {IET Control Theory and Applications},
author = {Chambon, E. and Burlion, L. and Apkarian, P.},
volume = {10},
number = {11},
pages = {1258-1268},
month = jul,
year = {2016},
url = {http://emmanuel-chambon.fr/assets/publis/IET_Chambon_2016.pdf}

}

International conferences

2015

Output to Input Saturation Transformation: demonstration and application to disturbed linear systems

Emmanuel Chambon, Laurent Burlion, Pierre Apkarian

In Proc. of the 54th IEEE Conference on Decision and Control, Osaka (Japan), pp. 7566-7571, 2015

AbstractShow/Hide BibTeXView online

Abstract

In the case of linear systems, control law design is often performed so that the resulting closed-loop meets specific frequency requirements. However, in many cases, it may be observed that the obtained controller does not enforce time-domain requirements amongst which the objective of keeping an output variable in a given interval. In this article, a transformation is proposed to convert expected bounds on an output variable into time-varying saturations on the synthesized linear control law. It is demonstrated that the resulting closed-loop is stable and satisfies time-domain constraints in the presence of unknown bounded disturbance. An application to a linear ball and beam model is presented.

@inproceedings{chambon_output2_2015,

address = {Osaka, Japan},
title = {Output to Input Saturation Transformation: demonstration and application to disturbed linear systems},
booktitle = {Proc. of the 54th IEEE Conference on Decision and Control},
author = {Chambon, E. and Burlion, L. and Apkarian, P.},
pages = {7566-7571},
month = dec,
year = {2015},
url = {http://emmanuel-chambon.fr/assets/publis/CDC_Chambon_2015.pdf}

}

Metzler matrix transform determination using a non-smooth optimization technique with an application to interval observers

Emmanuel Chambon, Pierre Apkarian, Laurent Burlion

In Proc. of the SIAM Conference on Control and its Applications, Paris (France), pp. 205-211, 2015

AbstractShow/Hide BibTeXView online

Abstract

The paper deals with the design of cooperative systems which formulates as computing a state coordinate transform such that the resulting dynamics are both stable and cooperative. The design of cooperative systems is a key problem to determine interval observers. Solutions are provided in the literature to transform any system into a cooperative system. A novel approach is proposed which reformulates into a stabilization problem. A solution is found using nonsmooth optimization techniques.

@inproceedings{chambon_metzler_2015,

address = {Paris, France},
title = {Metzler matrix transform determination using a non-smooth optimization technique with an application to interval observers},
booktitle = {Proc. of the SIAM Conference on Control and its Applications},
author = {Chambon, E. and Apkarian, P. and Burlion, L.},
pages = {205-211},
month = jul,
year = {2015},
url = {http://emmanuel-chambon.fr/assets/publis/SIAM_Chambon_2015.pdf}

}

Robust output interval constraint using O/I saturation transformation with application to uncertain linear launch vehicle

Emmanuel Chambon, Laurent Burlion, Pierre Apkarian

In Proc. of the 14th European Control Conference, Linz (Austria), pp. 1796-1801, 2015

AbstractShow/Hide BibTeX

Abstract

In this article, the case is considered where a regulated output of an uncertain system with unknown disturbance input is constrained to lie between two specified time-varying bounds. It is supposed a controller has already been designed using any desired technique. This controller may not satisfy expected output constraints. The objective is to design saturations on the control signal so that the closed-loop is altered only when those specifications are not met. The theory is presented in the linear case with linear dependence on an unknown disturbance. Application to an uncertain launcher linear model with unknown wind disturbance is presented.

@inproceedings{chambon_robust_2015,

address = {Linz, Austria},
title = {Robust output interval constraint using O/I saturation transformation with application to uncertain linear launch vehicle},
booktitle = {Proc. of the 14th European Control Conference},
author = {Chambon, E. and Burlion, L. and Apkarian, P.},
pages = {1796-1801},
month = jul,
year = {2015}

}

Flexible launch vehicle control using robust observer-based controller obtained through structured H-infty synthesis

Emmanuel Chambon, Pierre Apkarian, Laurent Burlion

In Proc. of the 3rd CEAS EuroGNC Conference, Toulouse (France), pp. 23-38, 2015

AbstractShow/Hide BibTeX

Abstract

Control of a flexible launch vehicle in the atmospheric ascent phase is highly challenging as it involves multiple concurrent design requirements. This ranges from reduction of the angle of attack in face of wind, minimum gain-phase and parametric margins as well as flexible modes attenuation. In this work, we discuss recently available non-smooth optimization techniques as a central tool to solve this problem. We consider designing an observer-based controller based on a Kalman filter suitably augmented with Dryden wind dynamics. We suggest a non-conservative approach to handle model uncertainties based upon multiple models of the launcher. This preliminary work aims at testing the potential of non-smooth controller tuning on a generic launcher model. It will serve as a stepping stone for a more in-depth study of the benchmark developed by M. Ganet at Airbus Defence and Space.

@inproceedings{chambon_flexible_2015,

address = {Toulouse, France},
title = {Flexible launch vehicle control using robust observer-based controller obtained through structured H-infty synthesis},
booktitle = {Proc. of the 3rd CEAS EuroGNC Conference},
author = {Chambon, E. and Apkarian, P. and Burlion, L.},
pages = {23-38},
month = apr,
year = {2015}

}

Seminars

2015

Détermination de matrice semblable Metzler par optimisation non lisse

Emmanuel Chambon

Seminar Onera DCSD, Toulouse (France), 2015

Abstract

@unpublished{seminar_onera_dcsd,

address = {Toulouse, France},
title = {D\'{e}termination de matrice semblable Metzler par optimisation non lisse},
booktitle = {Proc. of the Seminar Onera DCSD},
author = {Chambon, E.},
month = may,
year = {2015}

}

PhD Students Conferences

2015

Détermination de matrice semblable Metzler par optimisation non lisse

Emmanuel Chambon, Pierre Apkarian, Laurent Burlion

Accepted for presentation in the 6th Journées Doctorales / Journées Nationales MACS, Bourges (France), 2015

Pre-selected for extended version submission in Journal Européen des Systèmes Automatisés (special issue)

AbstractShow/Hide BibTeXView online

Abstract

La conception d'observateurs par intervalles repose sur la possibilité de rendre un système coopératif. Dans le cas linéaire, un système coopératif est un système dont la matrice d'état est à coefficients hors-diagonaux positifs. La littérature propose un certain nombre de méthodes pour concevoir des observateurs par intervalles sur des systèmes non coopératifs. Ces méthodes sont basées sur des changements de variables, le système étudié devenant coopératif dans les nouvelles coordonnées. Dans cet article, une méthode complémentaire au formalisme existant est présentée qui permet la détermination numérique de cette transformation sans hypothèse préalable. Elle repose sur une reformulation en problème de synthèse de loi de commande sur une collection de modèles. Le problème équivalent est alors résolu en faisant appel à une technique d'optimisation non lisse conçue pour ce type de problème de synthèse. L'approche est testée sur deux exemples extraits de la littérature.

@unpublished{chambon_determination_2015,

address = {Bourges, France},
title = {D\'{e}termination de matrice semblable Metzler par optimisation non lisse},
booktitle = {Proc. of the 6th Journ\'{e}es Doctorales / Journ\'{e}es Nationales MACS},
author = {Chambon, E. and Apkarian, P. and Burlion, L.},
note = {Pre-selected for extended version submission in Journal Européen des Systèmes Automatisés (special issue)},
month = jun,
year = {2015},
url = {http://emmanuel-chambon.fr/assets/publis/JDMACS_Chambon_2015.pdf}

}

Output– to Input–Saturation Transformation: application to a class of linear systems

Emmanuel Chambon, Laurent Burlion, Pierre Apkarian

Accepted for presentation in the 16th Congrès de l'Ecole Doctorale Systèmes, Toulouse (France), 2015

AbstractShow/Hide BibTeXView online

Abstract

This article presents ongoing work on the output– to input–saturation transformation (OIST). Given a linear system, a controller satisfying frequency requirements may not satisfy time-domain requirements on a considered regulated output. For example, one may expect an output variable to remain in a given interval. The proposed transformation is used to convert lateral constraints on the regulated output into saturations on the control. The OIST theory is here demonstrated and applied in the case of a specific class of linear systems. An application to the problem of crane control is presented.

@unpublished{chambon_output_2015,

address = {Toulouse, France},
title = {Output– to Input–Saturation Transformation: application to a class of linear systems},
booktitle = {Proc. of the 16th Congr\`{e}s de l'Ecole Doctorale Syst\`{e}mes},
author = {Chambon, E. and Burlion, L. and Apkarian, P.},
month = may,
year = {2015},
url = {http://emmanuel-chambon.fr/assets/publis/EDSYS_Chambon_2015.pdf}

}