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Design of Information Channels for Optimization and Stabilization in Networked Control

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Information and Control in Networks

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 450))

Abstract

In this chapter, we review some recent contributions and present new findings on the properties of information/measurement channels in stabilization and optimization problems in networked control. First, we discuss a finite horizon optimal control problem, and investigate structural and topological properties of such a problem over the space of information channels. Existence of optimal channels is discussed and structure and existence of optimal quantization policies is investigated, first for static settings and then for dynamic settings. We then consider the stabilization problem of open-loop unstable linear systems controlled over communication channels. We present tight necessary and sufficient conditions for stochastic stabilizability of such systems driven by Gaussian noise over channels. Stochastic stability notions include ergodicity and the existence of finite second moments. In the analysis, a partial order for optimization and a total order for stabilization are obtained on the set of channels and some research directions are presented.

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Acknowledgements

This research has been supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). Some of the figures in this chapter have appeared in [64] and [60].

The author is grateful to Giacomo Como, Bo Bernhardsson, and Anders Rantzer for hosting the workshop that took place in Lund University, which led to the publication of this book chapter. Some of the research reported in this chapter are results of the author’s collaborations with Tamer Başar, Tamás Linder, Sean Meyn, and Andrew Johnston. Discussions with Giacomo Como, Aditya Mahajan, Nuno Martins, Maxim Raginsky, Anant Sahai, Naci Saldi, Sekhar Tatikonda, Demos Teneketzis, and Tsachy Weissman are gratefully acknowledged.

This research was supported by LCCC—Linnaeus Grant VR 2007-8646, Swedish Research Council.

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  1. Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada, K7L 3N6

    Serdar Yüksel

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  1. Serdar Yüksel
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Correspondence to Serdar Yüksel .

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  1. Department of Automatic Control, Lund University, Lund, Sweden

    Giacomo Como

  2. Department of Automatic Control, Lund University, Lund, Sweden

    Bo Bernhardsson

  3. Department of Automatic Control, Lund University, Lund, Sweden

    Anders Rantzer

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Yüksel, S. (2014). Design of Information Channels for Optimization and Stabilization in Networked Control. In: Como, G., Bernhardsson, B., Rantzer, A. (eds) Information and Control in Networks. Lecture Notes in Control and Information Sciences, vol 450. Springer, Cham. https://doi.org/10.1007/978-3-319-02150-8_6

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  • DOI: https://doi.org/10.1007/978-3-319-02150-8_6

  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-02150-8

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