The Goh necessary optimality conditions for the Mayer problem with control constraints
Frankowska, Hélène; Tonon, Daniela (2013), The Goh necessary optimality conditions for the Mayer problem with control constraints, IEEE 52nd Annual Conference on Decision and Control (CDC), 2013 - Proceedings, IEEE, p. 538-543. http://dx.doi.org/10.1109/CDC.2013.6759937
TypeCommunication / Conférence
External document linkhttps://hal.archives-ouvertes.fr/hal-01067270
Conference titleIEEE 52nd Annual Conference on Decision and Control (CDC), 2013
Book titleIEEE 52nd Annual Conference on Decision and Control (CDC), 2013 - Proceedings
MetadataShow full item record
Abstract (EN)The well known Goh second order necessary optimality conditions in optimal control theory concern singular optimal controls taking values in the interior of a set of controls U. In this paper we investigate these conditions for the Mayer problem when U is a convex polytope or a closed subset of class C2 for an integrable optimal control u( ) that may take values in the boundary of U. This is indeed a frequent situation in optimal control and for this reason the understanding of this issue is crucial for the theory of second order optimality conditions. Applying the Goh transformation we derive necessary conditions on tangent subspace to U at u(t) for almost all t's. In the presence of an endpoint constraint, if the Mayer problem is calm, then similar second order necessary optimality conditions are satisfied whenever the maximum principle is abnormal. If it is normal, then analogous results hold true on some smaller subspaces.
Subjects / KeywordsMayer problem; Goh transformation; singular optimal control; maximum principle
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