Volume 14, Number 2, April-June 2008
|Page(s)||294 - 317|
|Published online||20 March 2008|
Inversion in indirect optimal control of multivariable systems
Centre Automatique et Systèmes, École Nationale Supérieure des Mines de Paris, 35 rue Saint-Honoré,
77305 Fontainebleau Cedex, France; firstname.lastname@example.org
2 Centre Automatique et Systèmes, École Nationale Supérieure des Mines de Paris, 60 bd Saint-Michel, 75272 Paris Cedex 06, France; email@example.com
Revised: 15 September 2006
This paper presents the role of vector relative degree in the formulation of stationarity conditions of optimal control problems for affine control systems. After translating the dynamics into a normal form, we study the Hamiltonian structure. Stationarity conditions are rewritten with a limited number of variables. The approach is demonstrated on two and three inputs systems, then, we prove a formal result in the general case. A mechanical system example serves as illustration.
Mathematics Subject Classification: 34C20 / 34H05 / 49K15 / 93C10 / 93C35
Key words: Optimal control / inversion / adjoint states / normal form
© EDP Sciences, SMAI, 2008
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