Towards Integrating Control and Information Theories: From by Song Fang, Jie Chen, Hideaki Ishii

By Song Fang, Jie Chen, Hideaki Ishii

This ebook investigates the functionality quandary matters in networked suggestions platforms. the truth that networked suggestions structures encompass keep an eye on and verbal exchange units and platforms demands the combination of keep watch over thought and knowledge conception. the first contributions of this booklet lie in features: the newly-proposed information-theoretic measures and the newly-discovered keep an eye on functionality barriers. We first suggest a couple of details notions to facilitate the research. utilizing these notions, sessions of functionality boundaries of networked suggestions structures, in addition to nation estimation platforms, are then investigated. normally, the ebook provides a special, cohesive remedy of functionality hassle problems with networked suggestions structures through an information-theoretic strategy. This e-book is thought to be the 1st to regard the aforementioned matters systematically and in a unified demeanour, providing a different viewpoint differing from latest books.

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Towards Integrating Control and Information Theories: From Information-Theoretic Measures to Control Performance Limitations

This publication investigates the functionality drawback matters in networked suggestions platforms. the truth that networked suggestions structures include regulate and conversation units and platforms demands the mixing of keep an eye on idea and data idea. the first contributions of this booklet lie in facets: the newly-proposed information-theoretic measures and the newly-discovered keep an eye on functionality boundaries.

Extra info for Towards Integrating Control and Information Theories: From Information-Theoretic Measures to Control Performance Limitations

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2 Power Gain We first consider SISO systems. 7 Consider a general causal system F as depicted in Fig. 2. Let its input process {xk } , xk ∈ R be a power signal. If the output process {yk } , yk ∈ R is also a power signal, then the power gain of the system from {xk } to {yk } is defined as Fig. 2 A general causal system y x Fig. 3 A general causal system with multiple inputs z x y 42 3 Control Performance Measures PG (F) pow (y) = sup sup pow(x)=0 pow (x) pow(x)=0 1 2π π −π Sy (ω) dω 1 2π π −π Sx (ω) dω .

25461. Note that the logarithm is with base 2 herein. 1 gives the negentropy for a wide class of random variables. The distributions include the triangular distribution, the exponential distribution, the double exponential distribution, the Rayleigh distribution, the Erlang distribution, and the Gamma distribution. We then define negentropy rate for asymptotically stationary processes. 10) where {xG (k)} , xG (k) ∈ Rm is a Gaussian process with the same asymptotic power spectrum as {xk }. The following proposition provides a key link between entropy domain analysis and frequency domain analysis of asymptotically stationary processes, by relating the negentropy rate to the asymptotic power spectrum.

Moreover, Rx (k) = 1 2π π −π Φx (ω) ejωk dω, and Rx (0) = 1 2π π −π Φx (ω) dω. Throughout this book, we deal with asymptotically stationary processes. Since stationarity can be viewed as a special case of asymptotic stationarity, all the results derived for asymptotically stationary processes are also valid for stationary processes. The following result [115] relates the power spectra of the input and output processes of a stable LTI system. 6 Consider an m-input, m-output stable LTI system with transfer function L (z).

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