| Issue |
ESAIM: COCV
Volume 14, Number 2, April-June 2008
|
|
|---|---|---|
| Page(s) | 294 - 317 | |
| DOI | https://doi.org/10.1051/cocv:2007054 | |
| Published online | 20 March 2008 | |
Inversion in indirect optimal control of multivariable systems
1
Centre Automatique et Systèmes, École Nationale Supérieure des Mines de Paris, 35 rue Saint-Honoré,
77305 Fontainebleau Cedex, France; chaplais@cas.ensmp.fr
2
Centre Automatique et Systèmes, École Nationale Supérieure des Mines de Paris, 60 bd
Saint-Michel, 75272 Paris Cedex 06, France; petit@cas.ensmp.fr
Received:
2
February
2006
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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