ESAIM: COCV, Vol. 14, N°2, pp. 294-317
DOI: 10.1051/cocv:2007054

Inversion in indirect optimal control of multivariable systems

François Chaplais¹ and Nicolas Petit<sup>2

1</sup>  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 February 2, 2006. Revised September 15, 2006. Published online October 13, 2007.)

Abstract
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


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