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Mathematics - Dynamical Systems & Differential Equations | Invariance Entropy for Deterministic Control Systems - An Introduction

Invariance Entropy for Deterministic Control Systems

An Introduction

Series: Lecture Notes in Mathematics, Vol. 2089

Kawan, Christoph

2013, XXII, 270 p. 2 illus., 1 illus. in color.

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  • 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

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.

Content Level » Research

Keywords » Controlled Invariance - Feedback Entropy - Invariance Entropy - Minimal Data Rates

Related subjects » Applications - Dynamical Systems & Differential Equations

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