Switchings of optimal controls and the equation ,
Symmetries and integrals of motion in optimal control
Symmetry analysis of the cylindrical Laplace equation.
Symmetry of minimizers with a level surface parallel to the boundary
We consider the functional where is a bounded domain and is a convex function. Under general assumptions on , Crasta [Cr1] has shown that if admits a minimizer in depending only on the distance from the boundary of , then must be a ball. With some restrictions on , we prove that spherical symmetry can be obtained only by assuming that the minimizer has one level surface parallel to the boundary (i.e. it has only a level surface in common with the distance). We then discuss how these...
Synthesis of optimal control for nonlinear third order systems [Book]
The Derivation of Cubic Splines with Obstacles by Methods of Optimization and Optimal Control.
The Euler equation for a class of nonconvex problems.
The Euler Lagrange Equation and the Pontriagin Maximum Principle
We consider the necessary conditions in the Calculus of Variations, expressed by the validity of the Euler Lagrange equation, or of the Pontriagin Maximum Principle; in particular, problems on multi-dimensional domanis are considered.
The evolution of dust emitted by a uniform source above ground level.
The generalization of the Du Bois-Reymond lemma for functions of two variables to the case of partial derivatives of any order
In the paper, the generalization of the Du Bois-Reymond lemma for functions of two variables to the case of partial derivatives of any order is proved. Some application of this theorem to the coercive Dirichlet problem is given.
The generalized Favard problem.
The H–1-norm of tubular neighbourhoods of curves
We study the H–1-norm of the function 1 on tubular neighbourhoods of curves in . We take the limit of small thicknessε, and we prove two different asymptotic results. The first is an asymptotic development for a fixed curve in the limit ε → 0, containing contributions from the length of the curve (at order ε3), the ends (ε4), and the curvature (ε5). The second result is a Γ-convergence result, in which the central curve may vary along the sequence ε → 0. We prove that a rescaled version of the...
The H–1-norm of tubular neighbourhoods of curves
We study the H–1-norm of the function 1 on tubular neighbourhoods of curves in . We take the limit of small thickness ε, and we prove two different asymptotic results. The first is an asymptotic development for a fixed curve in the limit ε → 0, containing contributions from the length of the curve (at order ε3), the ends (ε4), and the curvature (ε5). The second result is a Γ-convergence result, in which the central curve may vary along the sequence ε → 0. We prove that a rescaled version of...
The index of the second variation of a control system
The Lazy Travelling Salesman Problem in
We study a parameter (σ) dependent relaxation of the Travelling Salesman Problem on . The relaxed problem is reduced to the Travelling Salesman Problem as 0. For increasing σ it is also an ordered clustering algorithm for a set of points in . A dual formulation is introduced, which reduces the problem to a convex optimization, provided the minimizer is in the domain of convexity of the relaxed functional. It is shown that this last condition is generically satisfied, provided σ is large enough. ...
The linear control problem
The linear optimal control problem with variable endpoints.
The maximum principle in optimal control, then and now
The maximum Principle of optimal control: A history of ingenious ideas and missed opportunities
The minimal-norm problem and Pontriagin's maximum principle for Banach spaces, II