Finite-time partial stabilizability of chained systems

Chaker Jammazi

doi:10.1016/j.crma.2008.07.014

Optimal Control

Finite-time partial stabilizability of chained systems

Presented by: Alain Bensoussan

Chaker Jammazi ¹

¹ Laboratoire d'ingénierie mathématique, École polytechnique de Tunisie, B.P. 743, La Marsa 2078, Tunis, Tunisia

Comptes Rendus. Mathématique, Volume 346 (2008) no. 17-18, pp. 975-980.

Abstract (Original language)
Résumé

The Note deals with partial stabilization in finite-time of a class of nonlinear chained systems. It is well known that the chain of integrators of length n is not asymptotic stabilizable by continuous stationary feedback laws. This follows from the Brockett necessary condition for stabilizability. To overcome this limitation, we construct feedback laws that stabilize in finite-time the $(n - 1)$ first components of this chain of integrators while the last component converges. This special stabilization is obtained by continuous feedback laws and smooth outside the origin.

On considère des systèmes chaînés qui peuvent modéliser différents systèmes d'origine mécanique ou biologique. On sait depuis Brockett que cette classe de systèmes, qui est contrôlable, n'est pas stabilisable par des feedbacks statiques et continus. Pour contourner le problème, nous proposons l'approche de la stabilisation partielle en temps fini. Nous construisons dans ce travail des feedbacks permettant d'annuler en temps fini les $(n - 1)$ premières composantes tout en assurant la convergence de la dernière composante. Les feedbacks obtenus sont continus et réguliers en dehors de zéro.

Received: 2008-06-13
Accepted: 2008-07-10
Published online: 2008-08-20

DOI: 10.1016/j.crma.2008.07.014

Author's affiliations:

Chaker Jammazi ¹

¹ Laboratoire d'ingénierie mathématique, École polytechnique de Tunisie, B.P. 743, La Marsa 2078, Tunis, Tunisia

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Chaker Jammazi. Finite-time partial stabilizability of chained systems. Comptes Rendus. Mathématique, Volume 346 (2008) no. 17-18, pp. 975-980. doi : 10.1016/j.crma.2008.07.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.07.014/

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