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Research Papers

Stabilization of Markovian Jump Linear Systems With Log-Quantized Feedback

[+] Author and Article Information
Qing Xu

School of Transportation Science
and Engineering,
Beihang University,
Beijing 100191, China
e-mail: qingxu4@gmail.com

Chun Zhang

Extreme Networks, Inc.,
3306 NC Hwy 54,
Durham, NC 27709
e-mail: chunzhang@gmail.com

Geir E. Dullerud

Department of Mechanical Science
and Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: dullerud@illinois.edu

Simply put, the union of algebras generated by random variables up to the current time.

We denote Hi as the average gradient descendent direction for mode i.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received April 30, 2013; final manuscript received November 19, 2013; published online February 24, 2014. Assoc. Editor: Jongeun Choi.

J. Dyn. Sys., Meas., Control 136(3), 031019 (Feb 24, 2014) (10 pages) Paper No: DS-13-1177; doi: 10.1115/1.4026133 History: Received April 30, 2013; Revised November 19, 2013

This paper is concerned with mean-square stabilization of single-input Markovian jump linear systems (MJLSs) with logarithmically quantized state feedback. We introduce the concepts and provide explicit constructions of stabilizing mode-dependent logarithmic quantizers together with associated controllers, and a semi-convex way to determine the optimal (coarsest) stabilizing quantization density. An example application is presented as a special case of the developed framework, that of feedback stabilizing a linear time-invariant (LTI) system over a log-quantized erasure channel. A hardware implementation of this application on an inverted pendulum testbed is provided using a finite word-length approximation.

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Figures

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Fig. 2

An example of a 1-D log-controller

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Fig. 3

An LTI system over an unreliable channel with logarithmically quantized feedbacks

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Fig. 4

Trade-off between α and ρ

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Fig. 6

The model of Furuta pendulum

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Fig. 7

Trade-off between α and ρ

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Fig. 8

Trade-off among α, ρ, and θ

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Fig. 9

Comparison of the real test and simulation results

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Fig. 10

Zoomed-in comparison with no packet loss

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