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

Abstract

This thesis investigates the performance limitation issues in networked feedback systems. The fact that networked feedback systems consist of control and communication devices and systems calls for the integration of control theory and information theory.
As the title indicates, the primary contributions of this thesis lie in two main aspects: the newly-proposed information-theoretic measures and the newly-discovered system performance limitations.
We first propose a number of information-theoretic measures, including the negentropy rate as a measure of non-Gaussianity for stochastic processes, the Gaussianity-whiteness measure as a measure of Gaussianity and whiteness for stochastic processes and as a joint Shannon-Wiener entropy, the power gain as a worst-case disturbance attenuation measure, the entropy rate power as a generalization of entropy power, and the channel blurredness an alternative measure of channel quality to channel capacity. Additionally, spectral flatness is generalized from univariate processes to multivariate processes, and from signals to systems. Furthermore, “fire-quenching” channel power allocation policies, in stark contrast to conventional “water-filling” policies, are derived for many canonical channels, which are seen to be not only over space (channels) but also over time (channel states) and frequency.
Using those notions, three classes of performance limitations of (networked) feedback systems are then investigated, including Bode-type integrals as trade-offs in disturbance attenuation over the entire frequency range, power gain lower bounds as limitations in worst-case disturbance attenuation, and lower bounds in variance minimization, which lead to “uncertainty principles” for multiple-input, multiple-output systems. Implications of the limitations in the context of estimation systems are also examined.
The results presented in the thesis are expected to contribute to the understanding of the intrinsic limitations of (networked) feedback systems, the interplay of control theory and information theory, as well as the integrations of control systems and communication systems.

Date of Award	7 Sept 2015
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Jie CHEN (Supervisor)