GNECCO G.

Optimal control problems over an infinite number of decision stages are considered with emphasis on the deterministic scenario. Both the open-loop and the closed-loop formulations are given and conditions for the existence of a stationary optimal control law are provided. Unless strong assumptions are made on the dynamic system and on the...

In infinite-dimensional or functional optimization problems, one has to minimize (or maximize) a functional with respect to admissible solutions belonging to infinite-dimensional spaces of functions, often dependent on a large number of variables. As we consider optimization problems characterized by very general conditions, optimal solutions...

We report properties of fixed-structure parametrized (FSP) functions that give insights into the effectiveness of the "Extended Ritz Method" (ERIM) as a methodology for the approximate solution of infinite-dimensional optimization problems. First, we present the structure of some widespread FSP functions, including linear combinations of...

We consider discrete-time stochastic optimal control problems over a finite number of decision stages in which several controllers share different information and aim at minimizing a common cost functional. This organization can be described within the framework of "team theory." Unlike the classical optimal control problems,...

Discrete-time stochastic optimal control problems are considered. These problems are stated over a finite number of decision stages. The state vector is assumed to be observed through a noisy measurement channel. Because of the very general assumptions under which the problems are stated, obtaining analytically optimal solutions is practically...

First, well-known concepts from Statistical Learning Theory are reviewed. In reference to the problem of modelling an unknown input/output (I/O) relationship by fixed-structure parametrized functions, the concepts of expected risk, empirical risk, and generalization error are described. The last error is then split into approximation and...

This chapter describes the approximate solution of infinite-dimensional optimization problems by the "Extended Ritz Method" (ERIM). The ERIM consists in substituting the admissible functions with fixed-structure parametrized (FSP) functions containing vectors of "free" parameters. The larger the dimensions, the more accurate the approximations...

Two topics are addressed. The first refers to the numerical computation of integrals and expected values of functions that may depend on a large number of random variables. Of course, integration includes the computation of the expected values of functions dependent on random variables. However, the latter shows peculiar nontrivial aspects that...

This chapter addresses discrete-time deterministic problems, where optimal controls have to be generated at a finite number of decision stages. No random variables influence either the dynamic system or the cost function. Then, there is no necessity of estimating the state vector. Such optimization problems are stated for their intrinsic...

Discrete-time stochastic optimal control problems are stated over a finite number of decision stages. The state vector is assumed to be perfectly measurable. Such problems are infinite-dimensional as one has to find control functions of the state. Because of the general assumptions under which the problems are formulated, two approximation...

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The perceived Origin of full-body human Movement (OoM), i.e., the part of the body that is perceived by an external observer as the joint from which movement originates, represents a relevant topic for movement analysis. Indeed, its automated detection is important to contribute to the automated analysis of full-body emotions and of non-verbal...

Recently, an increasing research effort has been dedicated to analyse transmission and dispersion properties of periodic metamaterials containing resonators, and to optimize the amplitude of selected acoustic band gaps between consecutive dispersion curves in the Floquet-Bloch spectrum. Potential novel applications of this research are in the...

Multi-field asymptotic homogenization methods are proposed to describe the behaviour of periodic Cauchy materials subject to several physical phenomena, focusing on thermodiffusion. The resulting homogenized models provide the overall constitutive tensors and overall inertial terms. Moreover, they allow one to investigate the complex band...

In this work, a computational method is proposed to automatically investigate the perception of the origin of full-body human movement and its propagation. The method is based on a mathematical game built over a suitably defined graph structure representing the human body. The players of this game are the graph vertices, which form a subset of...

A game-theoretic approach based on the framework of transferable-utility cooperative games is developed to assess the reliability of transfer nodes in public transportation networks in the case of stochastic transfer times. A cooperative game is defined, whose model takes into account the public transportation system, the travel times, the...

The importance of transfer points in public transport networks is estimated by exploiting an approach based on transferable utility cooperative games, which integrates the network topology and the demands. Transfer points are defined as clusters of nearby stops, from which it is easily possible to switch between routes. The methodology is based...

A first order asymptotic homogenization technique is herein proposed for the investigation of wave propagation inside periodic microstructured viscoelastic metamaterials with local resonators. Specifically, in order to characterize the frequency band structure of the periodic metamaterials, an eigenvalue problem in terms of frequency-dependent...

In this work, the "effective dimension" of the output of the hidden layer of a one-hidden-layer neural network with random inner weights of its computational units is investigated. To do this, a polynomial approximation of the sigmoidal activation function of each computational unit is used, whose degree is chosen based both on a desired upper...

In the last years, various articles have dealt with the analysis of the Floquet-Bloch spectrum of periodic metamaterials containing resonators, and the optimization of selected acoustic band gaps between consecutive dispersion surfaces in that spectrum. Applications include opening/enlarging/closing/shifting band gaps in target acoustic...