Geodesic
Inversion in indirect optimal control of multivariable systems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 2, pp. 294-317

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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.

DOI : 10.1051/cocv:2007054
Classification : 34C20, 34H05, 49K15, 93C10, 93C35
Keywords: optimal control, inversion, adjoint states, normal form 
Petit, Nicolas; Chaplais, François. Inversion in indirect optimal control of multivariable systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 2, pp. 294-317. doi: 10.1051/cocv:2007054
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     title = {Inversion in indirect optimal control of multivariable systems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {294--317},
     year = {2008},
     publisher = {EDP-Sciences},
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     number = {2},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2007054/}
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