Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

Preface 1. Introduction Overview A Brief History of LMIs in Control Theory Notes on the Style of the Book Origin of the Book 2. Some Standard Problems Involving LMIs. Linear Matrix Inequalities Some Standard Problems Ellipsoid Algorithm Interior-Point Methods Strict and Nonstrict LMIs Miscellaneous Results on Matrix Inequalities Some LMI Problems with Analytic Solutions 3. Some Matrix Problems. Minimizing Condition Number by Scaling Minimizing Condition Number of a Positive-Definite Matrix Minimizing Norm by Scaling Rescaling a Matrix Positive-Definite Matrix Completion Problems Quadratic Approximation of a Polytopic Norm Ellipsoidal Approximation 4. Linear Differential Inclusions. Differential Inclusions Some Specific LDIs Nonlinear System Analysis via LDIs 5. Analysis of LDIs: State Properties. Quadratic Stability Invariant Ellipsoids 6. Analysis of LDIs: Input/Output Properties. Input-to-State Properties State-to-Output Properties Input-to-Output Properties 7. State-Feedback Synthesis for LDIs. Static State-Feedback Controllers State Properties Input-to-State Properties State-to-Output Properties Input-to-Output Properties Observer-Based Controllers for Nonlinear Systems 8. Lure and Multiplier Methods. Analysis of Lure Systems Integral Quadratic Constraints Multipliers for Systems with Unknown Parameters 9. Systems with Multiplicative Noise. Analysis of Systems with Multiplicative Noise State-Feedback Synthesis 10. Miscellaneous Problems. Optimization over an Affine Family of Linear Systems Analysis of Systems with LTI Perturbations Positive Orthant Stabilizability Linear Systems with Delays Interpolation Problems The Inverse Problem of Optimal Control System Realization Problems Multi-Criterion LQG Nonconvex Multi-Criterion Quadratic Problems Notation List of Acronyms Bibliography Index.

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Linear Matrix Inequalities in System and Control Theory

I have developed "tennis elbow" from lugging this book around the past four weeks, but it is worth the pain, the effort, and the aspirin. It is also worth the (relatively speaking) bargain price. Including appendixes, this book contains 894 pages of text. The entire panorama of the neural sciences is surveyed and examined, and it is comprehensive in its scope, from genomes to social behaviors. The editors explicitly state that the book is designed as "an introductory text for students of biology, behavior, and medicine," but it is hard to imagine any audience, interested in any fragment of neuroscience at any level of sophistication, that would not enjoy this book. The editors have done a masterful job of weaving together the biologic, the behavioral, and the clinical sciences into a single tapestry in which everyone from the molecular biologist to the practicing psychiatrist can find and appreciate his or

Principles of Neural Science

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Convex Analysisの二,三の進展について

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

Inputoutput finite time stabilization of linear systems.

This paper deals with the finite-time stability problem for continuous-time linear time-varying systems with finite jumps. This class of systems arises in many practical applications and includes, as particular cases, impulsive systems and sampled-data control systems. The paper provides a necessary and sufficient condition for finite-time stability, requiring a test on the state transition matrix of the system under consideration, and a sufficient condition involving two coupled differential/difference linear matrix inequalities. The sufficient condition turns out to be more efficient from the computational point of view. Moreover, it is the starting point for solving the stabilization problem, namely for finding a state feedback controller which finite-time stabilizes the closed loop system. Some examples illustrate the effectiveness of the proposed approach.

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Finite-time stability of linear time-varying systems with jumps: Analysis and controller design

http://wpage.unina.it/detommas/presentations/IFACSSSC_Slide.pdf

Input-output finite-time stabilization for a class of hybrid systems

This paper tackles the problem of Finite-Time Stability (FTS) and stabilization for the class of linear time-varying stochastic systems. In particular, we consider the case when the domains, where the state trajectories are required to belong in a given bounded time interval, do not contain the origin of the state-space. This can be the case of several applications, where the state values cannot go below a given threshold. For this class of systems, we present some sufficient conditions for FTS and FT stabilization via state feedback. These conditions are expressed in terms of differential linear matrix inequalities, or in terms of generalized differential Lyapunov equations. Extensive numerical simulations show that the proposed sufficient conditions are much less conservative than other conditions previously proposed in the literature.

Annular Finite-Time Stabilization of Stochastic Linear Time-Varying Systems

The aim of this work is to formulate a lumped parameters model of the venous tree of the lower limbs in order to study the effects and the possible clinical treatments for Chronic Venous Insufficiency (CVI). CVI is a pathology characterized by an important socio-economic impact due to its relevant prevalence, the costs for its diagnosis and treatment being more frequently widespread among the working population. The planning of haemodynamic surgical operations is critical to treat a pathological pattern of venous blood flow; such planning, in turn, depends on the right analysis of the possible consequences of flow modification. To this regard, the blood flow correction allows to solve the most important venous pathologies, in order to guarantee the restoration of normal blood flow by means of proper modifications of the venous tree. The developed model preserves the geometry of the venous network and considers some non linear resistive and capacitive effects. In fact, the study of the variability of some parameters (i.e. vessel radius) is very important to allow a correct diagnosis of vascular diseases. This variability causes a non linear behaviour of resistance and compliance effects. With the aid of the developed model we evaluate the time profile of blood velocity, flow and pressure in the entire venous network, both in physiological and pathological cases. The obtained results are discussed in comparison with available experimental data.

Francesco Amato

Papers

Inputoutput finite time stabilization of linear systems.

Finite-time stability of linear time-varying systems with jumps: Analysis and controller design

Input-output finite-time stabilization for a class of hybrid systems

Annular Finite-Time Stabilization of Stochastic Linear Time-Varying Systems

A nonlinear lumped parameters model to analyze the dynamics of venous reflux