Mathukumalli Vidyasagar - Böcker

System and Control theory is one of the most exciting areas of contemporary engineering mathematics. From the analysis of Watt's steam engine governor - which enabled the Industrial Revolution - to the design of controllers for consumer items, chemical plants and modern aircraft, the area has always drawn from a broad range of tools. It has provided many challenges and possibilities for interaction between engineering and established areas of 'pure' and 'applied' mathematics. This impressive volume collects a discussion of more than fifty open problems which touch upon a variety of subfields, including: chaotic observers, nonlinear local controlability, discrete event and hybrid systems, neural network learning, matrix inequalities, Lyapunov exponents, and many other issues. Proposed and explained by leading researchers, they are offered with the intention of generating further work, as well as inspiration for many other similar problems which may naturally arise from them. With extensive references, this book will be a useful reference source - as well as an excellent addendum to the textbooks in the area.

This brief introduces people with a basic background in probability theory to various problems in cancer biology that are amenable to analysis using methods of probability theory and statistics.  The title mentions “cancer biology” and the specific illustrative applications reference cancer data but the methods themselves are more broadly applicable to all aspects of computational biology. Aside from providing a self-contained introduction to basic biology and to cancer, the brief describes four specific problems in cancer biology that are amenable to the application of probability-based methods.  The application of these methods is illustrated by applying each of them to actual data from the biology literature. After reading the brief, engineers and mathematicians should be able to collaborate fruitfully with their biologist colleagues on a wide variety of problems.

Learning and Generalization provides a formal mathematical theory addressing intuitive questions of the type: • How does a machine learn a concept on the basis of examples?• How can a neural network, after training, correctly predict the outcome of a previously unseen input?• How much training is required to achieve a given level of accuracy in the prediction?• How can one identify the dynamical behaviour of a nonlinear control system by observing its input-output behaviour over a finite time?The second edition covers new areas including:• support vector machines;• fat-shattering dimensions and applications to neural network learning;• learning with dependent samples generated by a beta-mixing process;• connections between system identification and learning theory;• probabilistic solution of 'intractable problems' in robust control and matrix theory using randomized algorithms.It also contains solutions to some of the open problems posed in the first edition, while adding new open problems.

Learning and Generalization provides a formal mathematical theory for addressing intuitive questions of the type: * How does a machine learn a new concept on the basis of examples? * How can a neural network, after sufficient training, correctly predict the outcome of a previously unseen input? * How much training is required to achieve a specified level of accuracy in the prediction? * How can one identify the dynamical behaviour of a nonlinear control system by observing its input-output behaviour over a finite interval of time? The first edition, A Theory of Learning and Generalization, was the first book to treat the problem of machine learning in conjunction with the theory of empirical process, the latter being a well-established branch of probability theory. The treatment of both topics side-by-side leads to new insights, as well as new results in both topics.The second edition extends and improves upon this material, covering new areas including: * Support vector machines (SVM's) * Fat-shattering dimensions and applications to neural network learning * Learning with dependent samples generated by a beta-mixing process * Connections between system identification and learning theory * Probabilistic solution of 'intractable problems' in robust control and matrix theory using randomized algorithms It also contains solutions to some of the open problems posed in the first edition, while adding new open problems. This book is essential reading for control and system theorists, neural network researchers, theoretical computer scientists and probabilists The Communications and Control Engineering series reflects the major technological advances which have a great impact in the fields of communication and control. It reports on the research in industrial and academic institutions around the world to exploit the new possibilities which are becoming available

In this setting, the set of single-input, single-output (SISO) stable control systems is precisely the ring R, while the set of stable MIMO control systems is the set of matrices whose elements all belong to R.

In this setting, the set of single-input, single-output (SISO) stable control systems is precisely the ring R, while the set of stable MIMO control systems is the set of matrices whose elements all belong to R.