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Approximation of control problems involving ordinary and impulsive controls

Fabio CamilliMaurizio Falcone — 2010

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study an approximation scheme for a class of control problems involving an ordinary control , an impulsive control and its derivative u ˙ . Adopting a space-time reparametrization of the problem which adds one variable to the state space we overcome some difficulties connected to the presence of u ˙ . We construct an approximation scheme for that augmented system, prove that it converges to the value function of the augmented problem and establish an error estimates in ...

Homogenization of monotone systems of Hamilton-Jacobi equations

Fabio CamilliOlivier LeyPaola Loreti — 2010

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study homogenization for a class of monotone systems of first-order time-dependent periodic Hamilton-Jacobi equations. We characterize the Hamiltonians of the limit problem by appropriate cell problems. Hence we show the uniform convergence of the solution of the oscillating systems to the bounded uniformly continuous solution of the homogenized system.

A viscosity solution method for Shape-From-Shading without image boundary data

Emmanuel PradosFabio CamilliOlivier Faugeras — 2006

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we propose a solution of the Lambertian shape-from-shading (SFS) problem by designing a new mathematical framework based on the notion of viscosity solution. The power of our approach is twofolds: (1) it defines a notion of weak solutions (in the viscosity sense) which does not necessarily require boundary data. Moreover, it allows to characterize the viscosity solutions by their “minimums”; and (2) it unifies the works of [Rouy and Tourin, (1992) 867–884],...

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