A nonintersection property for extremals of variational problems with vector-valued functions
Aubry sets and the differentiability of the minimal average action in codimension one
Let (x,u,∇u) be a Lagrangian periodic of period 1 in x1,...,xn,u. We shall study the non self intersecting functions u: RnR minimizing ; non self intersecting means that, if u(x0 + k) + j = u(x0) for some x0∈Rn and (k , j) ∈Zn × Z, then u(x) = u(x + k) + jx. Moser has shown that each of these functions is at finite distance from a plane u = ρx and thus has an average slope ρ; moreover, Senn has proven that it is possible to define the average action of u, which is usually called since...
Continuous-time periodic systems in and . Part I: Theoretical aspects
The paper is divided in two parts. In the first part a deep investigation is made on some system theoretical aspects of periodic systems and control, including the notions of and norms, the parametrization of stabilizing controllers, and the existence of periodic solutions to Riccati differential equations and/or inequalities. All these aspects are useful in the second part, where some parametrization and control problems in and are introduced and solved.
Continuous-time periodic systems in and . Part II: State feedback problems
This paper deals with some state-feedback control problems for continuous time periodic systems. The derivation of the theoretical results underlying such problems has been presented in the first part of the paper. Here, the parametrization and optimization problems in , and mixed are introduced and solved.
Homogenization of periodic Finsler metrics.
Homogenization of periodic multi-dimensional structures
Si studia il comportamento asintotico di una classe di funzionali integrali che possono dipendere da misure concentrate su strutture periodiche multidimensionali, quando tale periodo tende a 0. Il problema viene ambientato in spazi di Sobolev rispetto a misure periodiche. Si dimostra, sotto ipotesi generali, che un appropriato limite può venire definito su uno spazio di Sobolev usuale usando tecniche di -convergenza. Il limite viene espresso come un funzionale integrale il cui integrando è caratterizzato...
Homogenization of unbounded functionals and nonlinear elastomers. The case of the fixed constraints set
The paper is a continuation of a previous work of the same authors dealing with homogenization processes for some energies of integral type arising in the modeling of rubber-like elastomers. The previous paper took into account the general case of the homogenization of energies in presence of pointwise oscillating constraints on the admissible deformations. In the present paper homogenization processes are treated in the particular case of fixed constraints set, in which minimal coerciveness hypotheses...
Homogenization of unbounded functionals and nonlinear elastomers. The case of the fixed constraints set
The paper is a continuation of a previous work of the same authors dealing with homogenization processes for some energies of integral type arising in the modeling of rubber-like elastomers. The previous paper took into account the general case of the homogenization of energies in presence of pointwise oscillating constraints on the admissible deformations. In the present paper homogenization processes are treated in the particular case of fixed constraints set, in which minimal coerciveness hypotheses...
On the analysis of periodic linear systems
Periodic stabilization for linear time-periodic ordinary differential equations
This paper studies the periodic feedback stabilization of the controlled linear time-periodic ordinary differential equation: ẏ(t) = A(t)y(t) + B(t)u(t), t ≥ 0, where [A(·), B(·)] is a T-periodic pair, i.e., A(·) ∈ L∞(ℝ+; ℝn×n) and B(·) ∈ L∞(ℝ+; ℝn×m) satisfy respectively A(t + T) = A(t) for a.e. t ≥ 0 and B(t + T) = B(t) for a.e. t ≥ 0. Two periodic stablization criteria for a T-period pair [A(·), B(·)] are established. One is an analytic criterion which is related to the transformation over time...
Strikte Konvexität für Variationsprobleme auf dem n-dimensionalen Torus.
Линейно-квадратичная задача оптимизации и частотная теорема для периодических систем. II.