NOLIACPA References

General references on NOLIACPA

· Glumineau et L. Graciani, "Symbolic nonlinear analysis and control package", Proc. 13^th IFACWorld Congress, vol. F, pp. 295-298 , San Francisco, California, USA, June 30 -- July 5, 1996, invited session.
- A. Glumineau, F. Plestan, C.H.Moog, " Symbolic Non Linear Analysis and Control Package", IMACS MultiConference : Computational Engineering in systems Applications, Lille, France, vol. 1, pp 30-32, 9-12 Juillet 1996, invited session.

· Laurent Graciani, Calcul Formel et Automatique non linéaire, D.E.A Automatique et Informatique Appliquée, Ecole Centrale de Nantes, , Encadreur A. Glumineau, 1994.
- Vincent Vignaud, Calcul Symbolique et Automatique non linéaire : NOLIACPA Master (D.E.A) Automatique et Informatique Appliquée, Encadreur A. Glumineau, 1997.

Routines references

Structural Analysis of non linear system

[Degre] Relative degre computation (SISO)

[Vectdegre] Relative degre computation (MIMO)

- Isidori, Alberto, Springer-Verlag, 2nd édition 1989, Nonlinear Control Systems, An introduction.

[Ordre] Computation of the minimal decoupling struture (essentiel orders)

- A. Glumineau and C.H. Moog, "The essential orders and the Nonlinear decoupling Problem", Int. J. Control, vol. 50, pp. 1825-1834, 1989.

[Interact] : Structure inversion algorithm

- M. Di Benedetto, A. Glumineau and C.H. Moog, "The Nonlinear Interactor and its Application to Input-Output Decoupling", I.E.E.E. Trans. Aut. Contr., AC-39, n°6, pp. 1246-1250, 1994.

[Obser] : Computation of observability indices

- G. Conte, A. M. Perdon, C. H. Moog, "Nonlinear Control System. An algebraic Approach", Springer Lecture Notes in Control and Information Sciences , Volume: 242 , ISBN/ISSN: 1-85233-151-8 , (1999) Springer – Verlag.

Accessibility condition test and input state linearization

[Resaccess] main routine for accessibility condition test and input state linearization

[Conshk] Computation of subspaces Hk ,k* and Hinfinite

[Conswi] Computation of Wi ( linearization forms)
[CNS] Computation of a full state input linearization n.s.c. by static feedback

[CS] Computation of a full state input linearization s.c. by dynamic feedback

[Access] Computation of accessibility indices

- E. ARANDA-BRICAIRE, C. H. MOOG, J.-B. POMET, « A linear algebraic framework for dynamic feedback linearization », IEEE Trans. Automat. Control , vol. 40, p. 127-132, 1995

- Eduardo Aranda Bricaire , Thèse de Docteur ès Sciences, Ecole Centrale de Nantes . Nantes Mai 1994, Linéarisation par bouclage des systèmes non-linéaires.

I/0 decouplability and static or dynamic compensator

[Rescomp] main routine for testing I/0 decouplability and static or dynamic compensator

[Interact] : Structure inversion algorithm

- M. Di Benedetto, A. Glumineau and C.H. Moog, "The Nonlinear Interactor and its Application to Input-Output Decoupling", I.E.E.E. Trans. Aut. Contr., AC-39, n°6, pp. 1246-1250, 1994.

Transformation of non linear systems and observer design

[Ss2de] : Transformation of an observable non linear state space equation to an Input/Output differential equation.

IOIA] Input-Output Injection linearizationAlgorithm

- F. Plestan, A. Glumineau, C.H. Moog, "Algebraic conditions for linearization by output injection", Proc. IFAC conf. Systems Structure & Control, Nantes, pp. 161-166, 5-7 Juillet 1995.

[IOIWDE] Input-Ouput Injection Without Differential Equation (without output derivatives):

- V. Lopez-M. and A. Glumineau, "Further results on linearization of nonlinear systems by input output injection" , Proc. 36th. IEEE CDC, vol. 1/5, pp. 652-653, San Diego, USA, December 10-12, 1997.

[GIOIAS] and [OGIOIAS] Generalized Input-Output Injection Algorithm for MISO system without or with Output Transformation :

- A. Glumineau, C.H. Moog, F. Plestan, "New algebro-geometric conditions for the linearization by input-output injection” , I.E.E.E. Trans. Aut. Contr., AC-41, n°4, pp. 598-603, 1996.

[GIOIA] Generalized Input-Output Injection Algorithm with output time derivatives :

- F. Plestan et A. Glumineau, "Linearization by generalized input-output injection", Systems Control Letters, vol. 31, pp. 115-128, 1997.

- V. Lopez-M., F. Plestan, A. Glumineau, "Linearization by Completely Generalized Input Ouput Injection", Kybernetika, vol.35, n° 6, pp. 793-802, 1999.

Tools for algebra computation

[ExtRank] computes the rank of a matrix. extrank is not restricted to rational entries.

[Exgausslim] based on the standard MAPLE `gausselim` procedure. Few changes are made to handle non-rational entries

- Harm van Essen, Faculteit Werktuigbouwkunde WFM 92.061, Technische Universiteit Eindhoven Juin 1992, Symbols speak louder than numbers

Routines not yet included in NOLIACPA

[SAT] Transformation of a MISO non linear system to an affine system

- A. Glumineau, V. Lopez-Morales, Transformation to State Affine System and observer design, New Directions in Nonlinear observer design, Lecture notes in Control and Information Sciences, Springer, vol. 244, ISBN1-85233-134-8., pp. 59-69, 1999.
- Souleiman, A. Glumineau, Equivalence and observers for state affine system, MTNS 2000, Mathematical Theory of Networks and systems, Perpignan, June 19-23, 2000.

- F. Desobry, G. Maillard, Développement en calcul formel d'une application pour l'observation des systèmes non linéaires, Projet de Spécialité, Option Automatique, Ecole Centrale de Nantes, 2000.

[DTA] Direct transformation of a MISO non linear system to an affine system
- I. Souleiman, A. Glumineau and G. Schreier, Direct Transformation of Nonlinear Systems into State Affine form. Nonlinear Control Systems, Proc. De NOLCOS'01, 5^th IFAC Symposium Nonlinear Control Systems, session invitée, pp. 545-551, St. Petersburg, Russia, 4-6 Juillet 2001.

- I. Souleiman, A. Glumineau and G. Schreier, Direct Transformation of Nonlinear Systems into State Affine Miso Form and Nonlinear Observers design, I.E.E.E. Trans. Aut. Contr , Vol.48, N° 12, 2191-2196, december, 2003.

-S. Hamaci, Algorithmes de l'Automatique non linéaire et calcul formel, DEA Automatique et Informatique appliquée, Ecole Centrale de Nantes, Encadreur A. Glumineau, 2002.

Routines to develop

Static Output feedback SISO Case

H.J.C. Huijberts, C. Moog et R. Pothin, Input-output decoupling of nonlinear systems by static measurement feedback, Systems and Control Letters,vol. 39,pp. 109-114.2000.
Keywords: Automatique theorique, Analyse des systemes de commande, Commande des processus, Theorie des systemes.

R. Pothin, Disturbance decoupling for a class of nonlinear MIMO systems by static measurement feedback, Systems and Control Letters,vol. 43,(2).pp. 111-116.2001.
Keywords: Nonlinear systems, time-delay systems, disturbance decoupling, dynamic compensation, static compensation.

R. Pothin, C. Moog et X. Xia, Disturbance decoupling of nonlinear MISO systems by static measurement feedback, Kybernetika,vol. 38,(5).pp. 601-608.2002,Special issue on "System Structure and Control".

(Extension to MIMO case to develop)