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Inversion in indirect optimal controlof multivariable systems

Published online by Cambridge University Press:  20 March 2008

François Chaplais  and
Nicolas Petit
François Chaplais
Affiliation:
Centre Automatique et Systèmes, École Nationale Supérieure des Mines de Paris, 35 rue Saint-Honoré, 77305 Fontainebleau Cedex, France; chaplais@cas.ensmp.fr
Nicolas Petit
Affiliation:
Centre Automatique et Systèmes, École Nationale Supérieure des Mines de Paris, 60 bd Saint-Michel, 75272 Paris Cedex 06, France; petit@cas.ensmp.fr
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Abstract

This paper presents the role of vector relative degree in theformulation of stationarity conditions of optimal control problemsfor affine control systems. After translating the dynamics into anormal form, we study the Hamiltonian structure. Stationarityconditions are rewritten with a limited number of variables. Theapproach is demonstrated on two and three inputs systems, then, weprove a formal result in the general case. A mechanical systemexample serves as illustration.

Keywords

Optimal controlinversionadjoint statesnormal form
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 14 , Issue 2 , April 2008 , pp. 294 - 317
Copyright
© EDP Sciences, SMAI, 2008

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