Displaying similar documents to “Asymptotics of accessibility sets along an abnormal trajectory”

Hölder equivalence of the value function for control-affine systems

Dario Prandi (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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We prove the continuity and the Hölder equivalence w.r.t. an Euclidean distance of the value function associated with the L cost of the control-affine system = () + ∑ (), satisfying the strong Hörmander condition. This is done by proving a result in the same spirit as the Ball–Box theorem for driftless (or sub-Riemannian) systems. The techniques used are based on a reduction of the control-affine system to a linear but time-dependent one,...

Sub-Riemannian sphere in Martinet flat case

A. Agrachev, B. Bonnard, M. Chyba, I. Kupka (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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This article deals with the local sub-Riemannian geometry on ℜ, () where is the distribution ker being the Martinet one-form : and is a Riemannian metric on . We prove that we can take as a sum of squares . Then we analyze the flat case where 1. We parametrize the set of geodesics using elliptic integrals. This allows to compute the exponential mapping, the wave front, the conjugate and cut loci and the sub-Riemannian sphere. A direct consequence of our computations is to...

Spreadability, Vulnerability and Protector Control

A. Bernoussi (2010)

Mathematical Modelling of Natural Phenomena

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In this work, we present some concepts recently introduced in the analysis and control of distributed parameter systems: , and . These concepts permit to describe many biogeographical phenomena, as those of pollution, desertification or epidemics, which are characterized by a spatio-temporal evolution

The structure of reachable sets for affine control systems induced by generalized Martinet sub-lorentzian metrics

Marek Grochowski (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we investigate analytic affine control systems q ˙ = ,  ∈  [] , where is an orthonormal frame for a generalized Martinet sub-Lorentzian structure of order of Hamiltonian type. We construct normal forms for such systems and, among other things, we study the connection between the presence of the singular trajectory starting at on the boundary of the reachable set from with the minimal number of analytic functions needed for...

Viability Kernels and Control Sets

Dietmar Szolnoki (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper analyzes the relation of viability kernels and control sets of control affine systems. A viability kernel describes the largest closed viability domain contained in some closed subset of the state space. On the other hand, control sets are maximal regions of the state space where approximate controllability holds. It turns out that the viability kernel of can be represented by the union of domains of attraction of chain control sets, defined relative to the given set . In...