Asymptotic rates of decay for some nonlinear ordinary differential equations and variational problems of arbitrary order
Asymptotics of accessibility sets along an abnormal trajectory
We describe precisely, under generic conditions, the contact of the accessibility set at time with an abnormal direction, first for a single-input affine control system with constraint on the control, and then as an application for a sub-riemannian system of rank 2. As a consequence we obtain in sub-riemannian geometry a new splitting-up of the sphere near an abnormal minimizer into two sectors, bordered by the first Pontryagin’s cone along , called the -sector and the -sector. Moreover we...
Asymptotics of accessibility sets along an abnormal trajectory
We describe precisely, under generic conditions, the contact of the accessibility set at time T with an abnormal direction, first for a single-input affine control system with constraint on the control, and then as an application for a sub-Riemannian system of rank 2. As a consequence we obtain in sub-Riemannian geometry a new splitting-up of the sphere near an abnormal minimizer γ into two sectors, bordered by the first Pontryagin's cone along γ, called the L∞-sector and the L2-sector. Moreover...
Begründung der Lagrange'schen Multiplicatorenmethode in der Variationsrechnung durch Vergleich derselben mit einer neuen Methode, welche zu den nämlichen Lösungen führt.
Begründung der Lagrange'schen Multiplicatorenmethode in der Variationsrechnung
Bemerkungen zur Variationsrechnung.
Casimir elements and optimal control
Classification générique de synthèses temps minimales avec cible de codimension un et applications
Conditions nécessaires et suffisantes d'existence de solutions en calcul des variations
Conjugate and cut loci of a two-sphere of revolution with application to optimal control
Conjugate gradient algorithm for optimal control problems with parameters
Conjugate-cut loci and injectivity domains on two-spheres of revolution
In a recent article [B. Bonnard, J.-B. Caillau, R. Sinclair and M. Tanaka, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26 (2009) 1081–1098], we relate the computation of the conjugate and cut loci of a family of metrics on two-spheres of revolution whose polar form is g = dϕ2 + m(ϕ)dθ2 to the period mapping of the ϕ-variable. One purpose of this article is to use this relation to evaluate the cut and conjugate loci for a family of metrics arising as a deformation of the round sphere and to determine...
Control problem for event-switched processes.
Curvature functionals for curves in the equi-affine plane
After having given the general variational formula for the functionals indicated in the title, the critical points of the integral of the equi-affine curvature under area constraint and the critical points of the full-affine arc-length are studied in greater detail. Notice. An extended version of this article is available on arXiv:0912.4075.
Curvature of optimal control: Deformation of scalar-input planar systems
Curvatures of single-input control systems
Die hinreichenden Bedingungen des Extremums in der Theorie des Mayerschen Problems. (Mit 3 Figuren im Text)
Die Lagrangesche Multiplikatorenregel in der Variationsrechnung für den Fall von gemischten Bedingungen und die zugehörigen Grenzgleichungen bei variabeln Endpunkten.
Discontinuous Hamiltonian flows for nonlinear control system.
Dynamic family of multicommodity inventory problems.