Path tracking with flatness and crone control for fractional systems

Abstract Flatness principles using polynomial matrices, well-suited for trajectory planning, are studied for fractional systems. Once a path has been defined by flatness for a real fractional system, a robust path tracking based on CRONE control is presented. Flatness in path planning is used to determine the controls to apply without integrating any differential equations.

[1]  K. B. Oldham,et al.  The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order , 1974 .

[2]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[3]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[4]  M. Fliess,et al.  Flatness and defect of non-linear systems: introductory theory and examples , 1995 .

[5]  A. Oustaloup La dérivation non entière , 1995 .

[6]  Hugues Mounier Proprietes structurelles des systemes lineaires a retards : aspects theoriques et pratiques , 1995 .

[7]  M. Fliess,et al.  Sur les systèmes linéaires à dérivation non entière , 1997 .

[8]  Robert M. Darling,et al.  On the Short‐Time Behavior of Porous Intercalation Electrodes , 1997 .

[9]  I. Podlubny Fractional differential equations , 1998 .

[10]  M. Fliess,et al.  On linear systems with a fractional derivation: introductory theory and examples , 1998 .

[11]  A. Oustaloup,et al.  La commande crone : du scalaire au multivariable , 1999 .

[12]  Philippe Martin,et al.  A Lie-Backlund approach to equivalence and flatness of nonlinear systems , 1999, IEEE Trans. Autom. Control..

[13]  A. Oustaloup,et al.  Utilisation de modèles d'identification non entiers pour la résolution de problèmes inverses en conduction , 2000 .

[14]  A. Oustaloup,et al.  Fractional Differentiation in Passive Vibration Control , 2002 .

[15]  Jean Lévine,et al.  Flat output characterization for linear systems using polynomial matrices , 2003, Syst. Control. Lett..

[16]  A. Oustaloup,et al.  Extension de la platitude aux systèmes fractionnaires {MIMO} : application à un système thermique , 2008 .

[17]  Alain Oustaloup,et al.  Flatness control for linear fractional {MIMO} systems: thermal application , 2008 .

[18]  Alain Oustaloup,et al.  Instrumental variable method with optimal fractional differentiation order for continuous-time system identification , 2009 .

[19]  S. Victor Identification par modèle non entier pour la poursuite robuste de trajectoire par platitude , 2010 .