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Research Papers

Adaptive Control of Linear Time-Varying Interval Systems

[+] Author and Article Information
Tayel Dabbous

Department of Electrical Engineering,
Higher Technological Institute,
Ramadan 10th City, Egypt
e-mail: tayel-dab@yahoo.com

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received March 20, 2016; final manuscript received January 24, 2017; published online June 5, 2017. Assoc. Editor: Yongchun Fang.

J. Dyn. Sys., Meas., Control 139(9), 091006 (Jun 05, 2017) (7 pages) Paper No: DS-16-1151; doi: 10.1115/1.4035927 History: Received March 20, 2016; Revised January 24, 2017

In this paper, we consider the adaptive control problem for a class of systems governed by linear time-varying interval differential equations having unknown (interval) parameters. Using the fact that system output posses lower and upper bounds, we have converted the interval differential equation into two sets of ordinary differential equations that describe the behavior of lower and upper bounds of system output. With this approach, interval analysis could be replaced by real analysis, and hence, adaptive control of interval systems can be treated as an ordinary adaptive control problem. Using variation arguments, we have developed the necessary conditions of optimality for the equivalent adaptive control problem. Finally, we present a numerical example to illustrate the effectiveness of the proposed (interval) control scheme.

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Figures

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Fig. 1

Lower and upper bounds for Xv and Yv (initial guess)

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Fig. 2

Lower and upper bounds for Xd and Xu (initial guess)

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Fig. 3

Lower and upper bounds for b1 and b1* (initial guess)

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Fig. 4

Lower and upper bounds for b3* and K1 (initial guess)

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Fig. 5

Lower and upper bounds for b4* and K2 (initial guess)

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Fig. 6

Lower and upper bounds for Xv and Yv (optimum)

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Fig. 7

Lower and upper bounds for Xd and Xu (optimum)

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Fig. 8

Lower and upper bound for b1 and b1* (optimum)

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Fig. 9

Lower and upper bounds for b3* and K1 (optimum)

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Fig. 10

Lower and upper bounds for b4* and K2 (optimum)

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