AN INTRODUCTION TO CONTROL SYSTEMS (2版)
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This significantly revised edition presents a broad introduction to Control Systems and balances new, modern methods with the more classical. It is an excellent text for use as a first course in Control Systems by undergraduate students in all branches of engineering and applied mathematics. The book contains: A comprehensive coverage of automatic control, integrating digital and computer control techniques and their implementations, the practical issues and problems in Control System design; the three-term PID controller, the most widely used controller in industry today; numerous in-chapter worked examples and end-of-chapter exercises. This second edition also includes an introductory guide to some more recent developments, namely fuzzy logic control and neural networks.
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Brownian Motion and Potential Theory, Modern and Classical (1版)
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【簡介】
In this book, potential theory is presented in an inclusive and accessible manner, with the emphasis reaching from classical to modern, from analytic to probabilistic, and from Newtonian to abstract or axiomatic potential theory (including Dirichlet spaces). The reader is guided through stochastic analysis featuring Brownian motion in its early chapters to potential theory in its latter sections. This path covers the following themes: martingales, diffusion processes, semigroups and potential operators, analysis of super harmonic functions, Dirichlet problems, balayage, boundaries, and Green functions.
The wide range of applications encompasses random walk models, especially reversible Markov processes, and statistical inference in machine learning models. However, the present volume considers the analysis from the point of view of function space theory, using Dirchlet energy as an inner product. This present volume is an expanded and revised version of an original set of lectures in the Aarhus University Mathematics Institute Lecture Note Series.
【目錄】
Contents:
Introduction
Martingales and Markov Processes
Brownian Motion and Ito-Calculus
Semi-Groups of Operators, Potentials, and Diffusion Equations
Harmonic Functions, Dynkin, and Transforms
Superharmonic Functions and Riesz Measures
Green Functions, Boundary Value Problems, and Kernels
Potential Theory, Capacity, Boundaries, Dirichlet Spaces, and Applications
Appendix: Kernels and More General Classes of Gaussian Processes
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