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Dive into the research topics where Alberto Tesi is active.

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Featured researches published by Alberto Tesi.


IEEE Transactions on Pattern Analysis and Machine Intelligence | 1992

On the problem of local minima in backpropagation

Marco Gori; Alberto Tesi

The authors propose a theoretical framework for backpropagation (BP) in order to identify some of its limitations as a general learning procedure and the reasons for its success in several experiments on pattern recognition. The first important conclusion is that examples can be found in which BP gets stuck in local minima. A simple example in which BP can get stuck during gradient descent without having learned the entire training set is presented. This example guarantees the existence of a solution with null cost. Some conditions on the network architecture and the learning environment that ensure the convergence of the BP algorithm are proposed. It is proven in particular that the convergence holds if the classes are linearly separable. In this case, the experience gained in several experiments shows that multilayered neural networks (MLNs) exceed perceptrons in generalization to new examples. >


Automatica | 1992

Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems

R. Genesio; Alberto Tesi

Abstract The paper considers the problem of determining the conditions under which a nonlinear dynamical system can give rise to a chaotic behaviour. On the basis of the harmonic balance principle, which is widely used in the frequency analysis of nonlinear control systems, two practical methods are presented for predicting the existence and the location of chaotic motions. This is formulated as a function of the system parameters, when the system structure is fixed by rather general input-output or state equation models. Several examples of application are presented to show the rather straightforward computations involved in the proposed methods, the kind of results which can be obtained and, due to the heuristic approach to the problem, their corresponding approximation.


IEEE Transactions on Automatic Control | 2005

Polynomially parameter-dependent Lyapunov functions for robust stability of polytopic systems: an LMI approach

Graziano Chesi; Andrea Garulli; Alberto Tesi; A. Vicino

In this note, robust stability of state-space models with respect to real parametric uncertainty is considered. Specifically, a new class of parameter-dependent quadratic Lyapunov functions for establishing stability of a polytope of matrices is introduced, i.e., the homogeneous polynomially parameter-dependent quadratic Lyapunov functions (HPD-QLFs). The choice of this class, which contains parameter-dependent quadratic Lyapunov functions whose dependence on the uncertain parameters is expressed as a polynomial homogeneous form, is motivated by the property that a polytope of matrices is stable if and only there exists an HPD-QLF. The main result of the note is a sufficient condition for determining the sought HPD-QLF, which amounts to solving linear matrix inequalities (LMIs) derived via the complete square matricial representation (CSMR) of homogeneous matricial forms and the Lyapunov matrix equation. Numerical examples are provided to demonstrate the effectiveness of the proposed approach.


Archive | 2009

Homogeneous Polynomial Forms for Robustness Analysis of Uncertain Systems

Graziano Chesi; Andrea Garulli; Alberto Tesi; Antonio Vicino

Positive Forms.- Positivity Gap.- Robustness with Time-varying Uncertainty.- Robustness with Time-invariant Uncertainty.- Robustness with Bounded-rate Time-varying Uncertainty.- Distance Problems with Applications to Robust Control.


IEEE Transactions on Automatic Control | 2003

Solving quadratic distance problems: an LMI-based approach

Graziano Chesi; Andrea Garulli; Alberto Tesi; Antonio Vicino

The computation of the minimum distance of a point to a surface in a finite-dimensional space is a key issue in several system analysis and control problems. The paper presents a general framework in which some classes of minimum distance problems are tackled via linear matrix inequality (LMI) techniques. Exploiting a suitable representation of homogeneous forms, a lower bound to the solution of a canonical quadratic distance problem is obtained by solving a one-parameter family of LMI optimization problems. Several properties of the proposed technique are discussed. In particular, tightness of the lower bound is investigated, providing both a simple algorithmic procedure for a posteriori optimality testing and a structural condition on the related homogeneous form that ensures optimality a priori. Extensive numerical simulations are reported showing promising performances of the proposed method.


Automatica | 1996

Harmonic balance analysis of period-doubling bifurcations with implications for control of nonlinear dynamics☆

Alberto Tesi; Eyad H. Abed; R. Genesio; Hua O. Wang

The harmonic balance method is applied to the analysis of period-doubling bifurcations in a general class of nonlinear feedback systems. Compact conditions for the prediction and stability analysis of period-doubling bifurcations are obtained. Specializations of these conditions for systems in which the nonlinear subsystem is static are given. The implications of the results to control design are illustrated through the development of a design procedure for solving a representative control problem. The objectives of the control design can include delay of a given period-doubling bifurcation as well as stability objectives. The results are illustrated with a detailed example.


Automatica | 2007

Brief paper: Robust stability of time-varying polytopic systems via parameter-dependent homogeneous Lyapunov functions

Graziano Chesi; Andrea Garulli; Alberto Tesi; Antonio Vicino

This paper deals with robust stability analysis of linear state space systems affected by time-varying uncertainties with bounded variation rate. A new class of parameter-dependent Lyapunov functions is introduced, whose main feature is that the dependence on the uncertain parameters and the state variables are both expressed as polynomial homogeneous forms. This class of Lyapunov functions generalizes those successfully employed in the special cases of unbounded variation rates and time-invariant perturbations. The main result of the paper is a sufficient condition to determine the sought Lyapunov function, which amounts to solving an LMI feasibility problem, derived via a suitable parameterization of polynomial homogeneous forms. Moreover, lower bounds on the maximum variation rate for which robust stability of the system is preserved, are shown to be computable in terms of generalized eigenvalue problems. Numerical examples are provided to illustrate how the proposed approach compares with other techniques available in the literature.


IEEE Transactions on Automatic Control | 1990

Computation of nonconservative stability perturbation bounds for systems with nonlinearly correlated uncertainties

A. Vicino; Alberto Tesi; Mario Milanese

Consideration is given to the problem of robust stability analysis of linear dynamic systems with uncertain physical parameters entering as polynomials in the state equation matrices. A method is proposed giving necessary and sufficient conditions for computing the uncertain system stability margin in parameter space, which provides a measure of maximal parameter perturbations preserving stability of the perturbed system around a known, stable, nominal system. A globally convergent optimization algorithm that enables solutions to the problem to be obtained is presented. Using the polynomial structure of the problem, the algorithm generates a convergent sequence of interval estimates of the global extremum. These intervals provide a measure of the accuracy of the approximating solution achieved at each step of the iterative procedure. Some numerical examples are reported, showing attractive features of the algorithm from the point of view of computational burden and convergence behavior. >


IEEE Transactions on Automatic Control | 1990

Robust stability of state-space models with structured uncertainties

Alberto Tesi; A. Vicono

A method for robust eigenvalue location analysis of linear state-space models affected by structured real parametric perturbations is proposed. The approach, based on algebraic matrix properties, deals with state-space models in which system matrix entries are perturbed by polynomial functions of a set of uncertain physical parameters. A method converting the robust stability problem into nonsingularity analysis of a suitable matrix is proposed. The method requires a check of the positivity of a multinomial form over a hyperrectangular domain in parameter space. This problem, which can be reduced to finding the real solutions of a system of polynomial equations, simplifies considerably when cases with one or two uncertain parameters are considered. For these cases, necessary and sufficient conditions for stability are given in terms of the solution of suitable real eigenvalue problems. >


Automatica | 1993

An overview of extremal properties for robust control of interval plants

Munther A. Dahleh; Alberto Tesi; Antonio Vicino

Abstract This paper provides an overview of recent results on the problem of robust stability and performance of feedback control systems in the presence of plant perturbations. The widely studied class of interval plants is considered, and an effort is made to cover different types of plant perturbations by incorporating, in addition to the interval plant description, unstructured norm bounded perturbations. Extremality results for these classes of uncertain systems are provided in a unifying framework. Robust performance of control systems is addressed in the paper and a number of extremal results are given for the computation of the structured singular value function for feedback systems with interval plants. Also, classical frequency response analysis for interval plant-controller families of open loop transfer functions is surveyed, with the aim of providing extremal results for the computation of specification parameters, such as phase or gain margins, and sensitivity and complementary sensitivity peaks.

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R. Genesio

University of Florence

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