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)

Technical Communique: Finite-time control of linear systems subject to parametric uncertainties and disturbances

Technical communique: Finite-time stabilization via dynamic output feedback

In this note, we consider the finite-time stabilization of discrete-time linear systems subject to disturbances generated by an exosystem. Finite-time stability can be used in all those applications where large values of the state should not be attained, for instance in the presence of saturations. The main result provided in the note is a sufficient condition for finite-time stabilization via state feedback. This result is then used to find some sufficient conditions for the existence of an output feedback controller guaranteeing finite-time stability. All the conditions are then reduced to feasibility problems involving linear matrix inequalities (LMIs). Some numerical examples are presented to illustrate the proposed methodology.

Finite-time control of discrete-time linear systems

In the last few years, robotics has been applied in clinical practice for a variety of laparoscopic procedures. This study reports our preliminary experience using robotics in the field of general surgery to evaluate the advantages and limitations of robot-assisted laparoscopy. Thirty-two consecutive patients were scheduled to undergo robot-assisted laparoscopic surgery in our units from March 2002 to July 2003. The indications were cholecystectomy, 20 patients; right adrenalectomy, two points; bilateral varicocelectomy, two points; Heller’s cardiomyotomy, two points; Nissen’s fundoplication, two points; total splenectomy, one point; right colectomy, one point; left colectomy, 1 point; and bilateral inguinal hernia repair, one point. In all cases, we used the da Vinci surgical system, with the surgeon at the robotic work station and an assistant by the operating table. Twenty-nine of 32 procedures (90.6%) were completed robotically, whereas three were converted to laparoscopic surgery. Conversion to laparoscopy was due in two patients to minor bleeding that could not be managed robotically and to robot malfunction in the third patient. There were no deaths. Median hospital stay was 2.2 days (range, 2–8). The main advantages of robot-assisted laparoscopic surgery are the availability of three-dimensional vision and easier instrument manipulation than can be obtain with standard laparoscopy. The learning curve to master the robot was ≥ 10 robotic procedures. The main limitations are the large diameter of the instruments (8 mm) and the limited number of robotic arms (maximum, three). We consider these technical shortcomings to be the cause for our conversions, because it is difficult to manage bleeding episodes with only two operating instruments. The benefit to the patient must be evaluated carefully and proven before this technology can become widely accepted in general surgery.

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Advantages and limits of robot-assisted laparoscopic surgery: preliminary experience.

The note deals with the finite-time analysis and design problems for continuous-time, time-varying linear systems. Necessary and sufficient conditions and a sufficient condition for finite-time stability are devised. Moreover, sufficient conditions for the solvability of both the state and the output feedback problems are stated. Such results require the feasibility of optimization problems involving Differential Linear Matrix Inequalities. Some numerical examples illustrate the effectiveness of the proposed approach.

Francesco Amato

Papers

Technical Communique: Finite-time control of linear systems subject to parametric uncertainties and disturbances

Technical communique: Finite-time stabilization via dynamic output feedback

Finite-time control of discrete-time linear systems

Advantages and limits of robot-assisted laparoscopic surgery: preliminary experience.

Finite-Time Stability of Linear Time-Varying Systems: Analysis and Controller Design