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Inversion in indirect optimal controlof multivariable systems

Published online by Cambridge University Press:  20 March 2008

François Chaplais
Affiliation:
Centre Automatique et Systèmes, École Nationale Supérieure des Mines de Paris, 35 rue Saint-Honoré, 77305 Fontainebleau Cedex, France; [email protected]
Nicolas Petit
Affiliation:
Centre Automatique et Systèmes, École Nationale Supérieure des Mines de Paris, 60 bd Saint-Michel, 75272 Paris Cedex 06, France; [email protected]
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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.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2008

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