Titlebook: Invariance Entropy for Deterministic Control Systems; An Introduction Christoph Kawan Book 2013 Springer International Publishing Switzerla

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Controllability, Lyapunov Exponents, and Upper Bounds,upper bounds for the invariance entropy in terms of Lyapunov exponents. These numbers measure the exponential rates of divergence for nearby trajectories, and hence are indicators for stability or instability of the system. In the entropy theory of classical dynamical systems, several relations betw

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Escape Rates and Lower Bounds, by a quantity which can be regarded as a uniform escape rate from the set .. Section 6.1 explains our basic approach which stems from Young [115]. In Sects. 6.2 and 6.3, two similar strategies how to derive explicit lower bounds from this approach are presented.

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978-3-319-01287-2Springer International Publishing Switzerland 2013

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Invariance Entropy for Deterministic Control Systems978-3-319-01288-9Series ISSN 0075-8434 Series E-ISSN 1617-9692

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Linear and Bilinear Systems,After we have introduced the notion of invariance entropy and studied its elementary properties, we now start to develop techniques for its computation or estimation. Before we turn our attention to smooth nonlinear systems, we look at linear and bilinear systems on Euclidean space.

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General Estimates, the invariance entropy. In particular, we can show that under appropriate compactness assumptions the outer invariance entropy of an admissible pair (., .) of a smooth system is finite, and an upper bound can be expressed in terms of a Lipschitz constant of the transition map and the upper capacitive dimension of ..