The minimum time function for the controlled Moreau's sweeping process

Let C(t), t 65 0 be a Lipschitz set-valued map with closed and (mildly non-)convex values and f (t, x, u) be a map, Lipschitz continuous w.r.t. x. We consider the problem of reaching a target S within the graph of C subject to the differential inclusion x 08 12N_{C(t)} (x) + G(t, x) starting \u307from x_0 08 C(t_0 ) in the minimum time T (t_0 , x_0 ). The dynamics is called a perturbed sweeping (or Moreau) process. We give sufficient conditions for T to be finite and continuous and characterize T through Hamilton\u2013Jacobi inequalities. Crucial tools for our approach are characterizations of weak and strong flow invariance of a set S subject to the inclusion. Due to the presence of the normal cone N_{C(t)} (x), the right-hand side of the inclusion contains implicitly the state constraint x(t) 08 C(t) and is not Lipschitz continuous with respect to x

A geometrically based criterion to avoid infimum-gaps in Optimal Control

In optimal control theory the expression infimum gap means a strictly negative difference between the infimum value of a given minimum problem and the infimum value of a new problem obtained by the former by extending the original family V of controls to a larger family W. Now, for some classes of domain-extensions -- like convex relaxation or impulsive embedding of unbounded control problems -- the normality of an extended minimizer has been shown to be sufficient for the avoidance of an infimum gaps. A natural issue is then the search of a general hypothesis under which the criterium 'normality implies no gap' holds true. We prove that, far from being a peculiarity of those specific extensions and from requiring the convexity of the extended dynamics, this criterium is valid provided the original family V of controls is abundant in the extended family W. Abundance, which is stronger than the mere C^0-density of the original trajectories in the set of extended trajectories, is a dynamical-topological notion introduced by J. Warga, and is here utilized in a 'non-convex' version which, moreover, is adapted to differential manifolds. To get the main result, which is based on set separation arguments, we prove an open mapping result valid for Quasi-Differential-Quotient (QDQ) approximating cones, a notion of 'tangent cone' resulted as a peculiar specification of H. Sussmann's Approximate-Generalized-Differential-Quotients (AGDQ) approximating cone

Un'analisi del modello di sviluppo brasiliano: cambiamento strutturale, specializzazione commerciale e le politiche per l'innovazione.

The dissertation deals with the Brazilian economic model and the role of the State in managing the economy through industrial and innovation policies. The first part of the dissertation is dedicated to the analysis of the productive structure and the international competitiveness of the Brazilian economy, while the second part focuses on the industrial and innovation policies implemented by the Brazilian government. An analysis of the economy\u201fs structural change is conducted, pointing out which sectors have gained importance in terms of manufacturing value added during the economic reforms of the \u201e90s and later on. A broad analysis of trade specialization is also conducted, and an investigation on the relationships between Brazil and its main trade partners is carried out, specifically focusing on China, currently its main trade partner. The trend in Foreign Direct Investments (FDI) flows is analysed, pointing out the increasing importance of the Brazilian multinationals in the international markets. In order to evaluate the sustainability of the economic model, a broad evaluation of the government industrial and innovation policies is conducted to assess the consistency of those policies with the structural problems of the economy. In particular, policies to improve the international trade performance are analysed. Furthermore, programmes and policies to strengthen the National Innovation System (NIS) are evaluated, and an in depth analysis of the NIS is also carried out. In addition, one chapter deals with an important agent of the Brazilian NIS: the National Development Bank (BNDES) and its role in the credit market. The increasing role of the State in managing the economy through industrial policies after several years of just \u201cfree markets\u201d policies is positively evaluated, although some structural economic problems still remain