Catálogo de publicaciones - libros

This paper is concerned with optimal control of semilinear stochastic evolution equations on Hilbert space driven by stochastic vector measure. Both continuous and discontinuous (measurable) vector fields are admitted. Due to nonexistence of regular solutions, existence and uniqueness of generalized (or measure valued) solutions are proved. Using these results, existence of optimal feedback controls from the class of bounded Borel measurable maps are proved for several interesting optimization problems.

We study the local exponential stabilization of the 3D Navier-Stokes equations in a bounded domain, around a given steady-state flow, by means of a boundary control. We look for a control so that the solution to the Navier-Stokes equation be a strong solution. In the 3D case, such solutions may exist if the Dirichlet control satisfies a compatibility condition with the initial condition. In order to determine a feedback law satisfying such a compatibility condition, we consider an extended system coupling the Navier-Stokes equations with an equation satisfied by the control on the boundary of the domain. We determine a linear feedback law by solving a linear quadratic control problem for the linearized extended system. We show that this feedback law also stabilizes the nonlinear extended system.

Similar evolutionary variational inequalities appear as variational formulations of continuous models for sandpile growth, magnetization of type-II superconductors, and evolution of some other dissipative systems characterized by the multiplicity of metastable states, long-range interactions, avalanches, and hysteresis. Such formulations for sandpile and superconductor models are, however, convenient for modeling only some of the variables (evolving pile shape and magnetic field for sandpile and superconductor models, respectively). The conjugate variables (the surface sand flux and the electric field) are also of interest in various applications. Here we derive dual variational formulations, similar to mixed variational inequalities in plasticity, for the sandpile and superconductor models. These formulations are used in numerical simulations and allow us to approximate simultaneously both the primary and dual variables.

The paper is concerned with the dynamic modelling of the unconventional remotely-piloted Lighter-Than-Air vehicle patented by Nautilus S.p.A. and the Polytechnic of Turin. The airship mathematical model is based on a 6 degree-of-freedom nonlinear model referring to the basic Newtonian mechanics. Emphasis is placed on those innovative and peculiar aspects of the dynamic modelling, such as aerodynamics, buoyancy and inertial features.

The synthesis of an array antenna is an inverse problem. The solution of this problem is the optimization of the complex excitation law of the antenna’s radiating elements and the shape of the antenna which provides a specified radiation pattern. The general character of this method permits to find numerous application in civil and military areas (satellites, telecommunication for earth mobiles, radar antennas, etc ...).

In many physical applications, the evolution of the system is endowed with dynamical boundary conditions , i.e., with boundary operators containing time derivatives. In this paper we discuss a generalization of such systems, where stochastic perturbations affect the way the system evolves in the interior of the domain as well as on the boundary.

The main goal of this paper is to establish the uniqueness of solutions of finite energy for a classical dynamic nonlinear thin shallow shell model with clamped boundary conditions. The static representation of the model is an extension of a Koiter shallow shell model. Until now, this has been an open problem in the literature. The primary difficulty is due to a lack of regularity in the nonlinear terms. Indeed the nonlinear terms are not locally Lipshitz with respect to the energy norm. The proof of the theorem relies on sharp PDE estimates that are used to prove uniqueness in a lower topology than the space of finite energy.

A non-autonomous sub-Riemannian problem is considered: Since periodicity with respect to the independent variable is assumed, one can define the averaged problem. In the case of the minimization of the energy, the averaged Hamiltonian remains quadratic in the adjoint variable. When it is non-degenerate, a Riemannian problem and the corresponding metric can be uniquely associated to the averaged problem modulo the orthogonal group of the quadratic form. The analysis is applied to the controlled Kepler equation. Explicit computations provide the averaged Hamiltonian of the Kepler motion in the three-dimensional case. The Riemannian metric is given, and the curvature of a special subsytem is evaluated.

We discuss error estimates for the numerical analysis of Neumann boundary control problems. We present some known results about piecewise constant approximations of the control and introduce some new results about continuous piecewise linear approximations. We obtain the rates of convergence in L ^2(Γ). Error estimates in the uniform norm are also obtained. We also discuss the semidiscretization approach as well as the improvement of the error estimates by making an extra assumption over the set of points corresponding to the active control constraints.

In this paper, we consider the time minimal problem for an Autonomous Underwater Vehicle. We investigate, on a simplified model, the existence of singular extremals and discuss their optimality status. Moreover, we prove that singular extremals corresponding to the angular acceleration are of order 2. We produce in this case a semi-canonical form of our Hamiltonian system and we can conclude the existence of chattering extremals..