Decomposition, Well-Posedness and Stability
InhaltsverzeichnisMathematical preliminaries.Gain and dissipativity.Decomposition of large-scale interconnected systems.Well-posedness of large-scale interconnected systems.Small-gain type criteria for LP-stability.Dissipativity-type criteria for L2-stability.L2-Instability criteria.L?-stability and ?-instability using exponential weighting.
A Theory of 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 output 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? This is the first book to treat the problem of machine learning in conjunction with the theory of empirical processes, 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. An extensive references section and open problems will help readers to develop their own work in the field.
How does a machine learn a new concept on the basis of examples? This second edition takes account of important new developments in the field. It also deals extensively with the theory of learning control systems, now comparably mature to learning of neural networks.
Exploring the principles of learning and generalization, this book delves into how knowledge is acquired and applied across different contexts. It examines various learning theories, emphasizing their implications for education and cognitive development. The text also discusses the role of experience in shaping understanding and the importance of adaptability in applying learned concepts to novel situations. Through a blend of theoretical insights and practical applications, readers gain a comprehensive understanding of the mechanisms behind learning processes.
Focusing on the intersection of probability theory and cancer biology, this brief provides insights into various problems within the field that can be analyzed using statistical methods. While it highlights specific applications related to cancer data, the techniques discussed are applicable to a wider range of computational biology issues, making it a valuable resource for those with foundational knowledge in probability looking to explore its relevance in biological research.
The book presents the stable factorization approach for designing feedback controllers in linear control systems, focusing on multi-input, multi-output (MIMO) plants represented as matrices over a commutative ring. It defines stable control systems within this mathematical framework and introduces the concept of coprimeness for matrices, which extends to various system types. A key result is the parametrization of stabilizing controllers using a single parameter from the ring, facilitating the formulation of stabilization problems. This reprint revisits foundational concepts in control system synthesis.