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adjoint states

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Inversion in indirect optimal controlof multivariable systems
François Chaplais, Nicolas Petit
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 14 / Issue 2 / April 2008

Published online by Cambridge University Press:

20 March 2008, pp. 294-317

Print publication:

April 2008
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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.