Invariance Entropy for Deterministic Control Systems
An Introduction
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Beschreibung
This monograph provides an introduction to the concept of invariance entropy, the central motivation of which lies in the need to deal with communication constraints in networked control systems. For the simplest possible network topology, consisting of one controller and one dynamical system connected by a digital channel, invariance entropy provides a measure for the smallest data rate above which it is possible to render a given subset of the state space invariant by means of a symbolic coder-controller pair. This concept is essentially equivalent to the notion of topological feedback entropy introduced by Nair, Evans, Mareels and Moran (Topological feedback entropy and nonlinear stabilization. IEEE Trans. Automat. Control 49 (2004), 1585–1597). The book presents the foundations of a theory which aims at finding expressions for invariance entropy in terms of dynamical quantities such as Lyapunov exponents. While both discrete-time and continuous-time systems are treated, the emphasis lies on systems given by differential equations.
This monograph provides an introduction to the concept of invariance entropy, the central motivation of which lies in the need to deal with communication constraints in networked control systems. For the simplest possible network topology, consisting of one controller and one dynamical system connected by a digital channel, invariance entropy provides a measure for the smallest data rate above which it is possible to render a given subset of the state space invariant by means of a symbolic coder-controller pair. This concept is essentially equivalent to the notion of topological feedback entropy introduced by Nair, Evans, Mareels and Moran (Topological feedback entropy and nonlinear stabilization. IEEE Trans. Automat. Control 49 (2004), 1585–1597). The book presents the foundations of a theory which aims at finding expressions for invariance entropy in terms of dynamical quantities such as Lyapunov exponents. While both discrete-time and continuous-time systems are treated, the emphasis lies on systems given by differential equations.
The first book to present results on the relatively new notions of feedback and invariance entropy Provides detailed proofs of all key results, together with a comprehensive exposition of the mathematical background material used therein Will be particularly interesting for readers with a background in dynamical systems theory The basic knowledge of control theory needed for its understanding is presented at great length in the first chapter Includes supplementary material: sn.pub/extras
Autor*in
Christoph Kawan
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Controlled Invariance Feedback Entropy Invariance Entropy Minimal Data Rates
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From the book reviews:
“The topics are well organized, the exposition is clear and there are examples to illustrate the theoretical results. This book is highly recommended for both researchers and graduate students in dynamical systems, control theory and related areas. This book is particularly useful because it collects in one place a large number of seminal results that are essential for an understanding of invariance entropy.” (Alexandre José Santana, Mathematical Reviews, August, 2014)()