127
Views
2
CrossRef citations to date
0
Altmetric
Flat Systems of Finite Dimension

Classical electrical engineering questions in the light of Fliess's differential algebraic framework of non-linear control systems

Pages 382-397 | Received 07 Jul 2007, Accepted 08 Jul 2007, Published online: 06 Oct 2010

References

  • Aït-Amirat , Y . 1994 . “Contribution à la théorie de la structure des systèmes en automatique. Application au découplage et au rejet de perturbations” . In Thèse de doctorat , Université Claude Bernard-Lyon I .
  • Bass , H , Buium , A and Cassidy , PJ . 1999 . Selected Works of Ellis Kolchin with Commentary , Providence, RI : American Mathematical Society .
  • Boulier , F . 1994 . “ Étude et implantation de quelques algorithmes en algèbre différentielle” . In Thèse de doctorat , Université des sciences et technologies de Lille .
  • Boulier , F and Petitot , M . 1995 . “Complete computation of the relations for implicit dynamical systems” . In Prepr. of the IFAC Conference on System Structure and Control , Edited by: Guglielmi , M . 635 – 639 . France : Nantes .
  • Conte , G , Moog , CH and Perdon , AM . 1999 . Nonlinear Control Systems: An Algebraic Setting , Sci., London : Springer-Verlag . 243 of Lecture Notes in Control and Inform
  • Conte , G , Perdon , AM and Moog , CH . 1993 . The differential field associated to a general analytic nonlinear dynamical system . IEEE Trans. Automat. Contr. , 38 : 1120 – 1124 .
  • Delaleau , E . 1993 . “ Sur les dérivées de l’entrée en représentation et commande des systèmes non linéaires. ” . In Thèse de doctorat , Université Paris XI .
  • Delaleau , E . 2002 . “Algèbre différentielle” . In Mathématiques pour les systèmes dynamiques , Edited by: Richard , JP . 245 – 268 . Paris : Hermès . Chap. 6, Coll. Information, Commande, Communication
  • Delaleau , E . 2003 . “Automatique nonlinéaire: de la théorie aux applications en commande des systèmes électromécaniques” . In Mémoire d’habilitation à diriger des recherches , Université Paris XI .
  • Delaleau , E and Pereira da Silva , PS . 1998a . Filtrations in feedback synthesis: part I — systems and feedbacks . Forum Math. , 10 : 147 – 174 .
  • Delaleau , E and Pereira da Silva , PS . 1998b . Filtrations in feedback synthesis: part II — input–output and disturbance decoupling . Forum Math. , 10 : 259 – 276 .
  • Delaleau , E and Respondek , W . 1998 . Lowering the orders of derivatives of controls in generalized state space systems . J. Math. Syst. Estim. Contr. , 8 : 427 – 453 .
  • Diop , S . 1989 . “Théorie de l’élimination et principe du modèle interne en automatique” . In Thèse de doctorat , Université Paris XI .
  • Diop , S . 1991 . Elimination in control theory . Math. Contr. Signals Syst. , 4 : 17 – 32 .
  • Diop , S . 1992 . Differential-algebraic decision methods and some applications to system theory . Theo. Comput. Sci. , 93 : 137 – 161 .
  • Diop , S . 1993 . Closedness of morphisms of differential algebraic sets. Applications to system theory . Forum Math. , 5 : 33 – 47 .
  • Asmi , SEl . 1992 . “Autour de l’inversion des systèmes entrée-sortie et du concept d’essentialité: une approche algébrique” . In Thèse de doctorat , Université Paris XI .
  • Fliess , M . 1986a . A note on the invertibility of nonlinear input-output differential systems . Syst. Contr. Lett. , 8 : 147 – 151 .
  • Fliess , M . 1986b . “Some remarks on nonlinear invertibility and dynamic state-feedback” . In Theory and Applications of Nonlinear Control Systems (Proc. MTNS, 1985) , Edited by: Byrnes , CI and Linquist , A . 115 – 121 . Amsterdam, , North-Holland : Elsevier Science Publishers B.V. .
  • Fliess , M . 1989a . Automatique et corps différentiels . Forum Math. , 1 : 227 – 238 .
  • Fliess , M . 1989b . Generalized linear systems with lumped or distributed parameters and differential vector spaces . Int. J. Contr. , 49 : 1989 – 1999 .
  • Fliess , M . 1990a . Automatique en temps discret et algèbre aux différences . Forum Math. , 2 : 213 – 232 .
  • Fliess , M . 1990b . Generalized controller canonical form for linear and nonlinear dynamics . IEEE Trans. Automat. Contr. , 35 : 994 – 1001 .
  • Fliess , M . 1990c . Some basic structural properties of generalized linear systems . Syst. Contr. Lett. , 15 : 391 – 396 .
  • Fliess , M . 1990d . What is the Kalman state variable representation good for? . Proc. 29th IEEE Conference on Decision and Control . 1990d , Honolulu. pp. 1282 – 1287 .
  • Fliess , M . 1992 . Reversible linear and nonlinear discrete-time dynamics . IEEE Trans. Automat. Contr. , 37 : 1144 – 1153 .
  • Fliess , M and Glad , ST . 1993 . “An algebraic approach to linear and nonlinear control” . In Essays on Control: Perspectives in the Theory and its Applications (Groningen, 1993), 14 of Progr. Systems Control Theory , 223 – 265 . Boston, MA : Birkhäuser .
  • Fliess , M and Hasler , M . 1990 . “Questioning the classic state-space description via circuit examples” . In Realization and Modelling in System theory (MTNS, 1989) , Edited by: Kaashock , MA , van Shuppen , JH and Ran , ACM . 1 – 12 . Boston, MA : Birkhäuser . xx of Progr. Systems Control Theory
  • Fliess , M , Lévine , J , Martin , P and Rouchon , P . 1992 . Sur les systèmes non linéaires différentiellement plats . C. R. Acad. Sci. Paris Sér. I Math. , 315 : 619 – 624 .
  • Fliess , M , Lévine , J and Rouchon , P . 1993 . Generalized state variable representation for a simplified crane description . Int. J. Contr. , 85 : 277 – 283 .
  • Fliess , M , Lévine , J , Martin , P and Rouchon , P . 1995 . Flatness and defect of non-linear systems: introductory theory and examples . Int. J. Contr. , 61 : 1327 – 1361 .
  • Glad , ST . 1988 . “Nonlinear state space and input output description using differential polynomials” . In New Trends in Nonlinear Control Theory , Edited by: Descusse , J , Fliess , M , Isidori , A and Leborgne , D . 182 – 189 . Heidelberg : Springer-Verlag . 122 of Lecture Notes in Control and Inform. Sci.
  • Glad , ST . 1990 . “Differential algebraic modelling of nonlinear systems” . In Realization and modelling in system theory (Amsterdam, 1989), 3 of Progr. Systems Control Theory , 97 – 105 . Boston, MA : Birkhäuser .
  • Johnson , J . 1969a . Differential dimension polynomials and a fundamental theorem on differential modules . Amer. J. Math , 91 : 239 – 248 .
  • Johnson , J . 1969b . Kähler differentials and differential algebra . Trans. Amer. Math. Soc. , 89 : 92 – 98 .
  • Kolchin , ER . 1973 . Differential Algebra and Algebraic Groups , New York : Academic Press .
  • Krause , PC and Wasynczuk , O . 1989 . Electromechanical Motion Devices , New York : McGraw-Hill Book Company .
  • Leonhard , W . 1996 . Control of Electrical Drives , Berlin Heidelberg : Springer-Verlag .
  • Martin , P and Rouchon , P . 1998 . Personnal communication ,
  • Messager , F . 1992 . “Sur la stabilisation discontinue des systèmes” . In Thèse de doctorat , Université Paris XI .
  • Mounier , H . 1995 . “Propriétés structurelles des systèmes linéaires à retards: aspects théoriques et pratiques” . In Thèse de doctorat , Université Paris XI .
  • Novotny , DW and Lipo , TA . 1996 . Vector Control and Dynamics of AC Drives , Oxford : Clarendon Press .
  • Ollivier , F . 1990 . “Le problème de l’identifiabilité structurelle globale: approche théorique, méthodes effectivesé et bornes de complexité” . Thèse de doctorat, École polytechnique ,
  • Park , RH . 1929 . Two reaction theory of synchronous machines—generalized method of analysis—part I . AIEE Trans. , 48 : 716 – 727 .
  • Pereira da Silva , PS and Delaleau , E . 2001 . Algebraic necessary and sufficient conditions of input–output linearization . Forum Math. , 13 : 335 – 357 .
  • Ritt , JF . 1950 . Differential Algebra , New York : American Mathematical Society .
  • Rudolph , J . 1991 . “Poursuite de modèle: une approche par l’algèbre différentielle” . In Thèse de doctorat , Université Paris XI .
  • Rudolph , J . 1994 . Viewing input-output system equivalence from differential algebra . J. Math. Syst. Estim. Contr. , 4 : 353 – 383 .
  • Rudolph , J . 2003 . Beiträge zur flachheitsbasierten Folgeregelung linearer und nichtlinearer Systeme endlicher und unendlicher Dimension , Aachen : Shaker Verlag .
  • Sedoglavic , A . 2001 . “Méthodes seminumériques en algèbre différentielle; application à l’étude des propriétés structurelles de systèmes différentiels algébriques en automatique” . Thèse de doctorat, École polytechnique ,
  • Sira-Ramírez , H . 1991 . Nonlinear dynamical feedback controlled descent on a non atmosphere-free planet: a differentiel algebraic approach . Contr. Theo. Adv. Tech. , 7 : 301 – 320 .
  • Sira-Ramírez , H . 1992 . The differentiel algebraic approach in nonlinear dynamical feedback controlled landing maneuvers . IEEE Trans. Automat. Contr. , 37 : 518 – 524 .
  • Sira-Ramírez , H and Lischinsky-Arenas , P . 1991 . The differentiel algebraic approach in nonlinear dynamical conpensator design for DC-to-DC power converters . Int. J. Contr. , 54 : 111 – 134 .
  • van der Waerden , BL . 1991a . Algebra, I , New York : Springer-Verlag .
  • van der Waerden , BL . 1991b . Algebra, II , New York : Springer-Verlag .
  • Wey , T and Svaricek , F . 1995 . Analyse und Synthese nichlinearer Regelungssysteme mittels Differentialalgebre . Automatisierungstechnik , 43 : 163 – 203 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.