PARISINI T.

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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