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.
Adaptive Control of Linear Time-Varying Interval Systems
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.
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Dabbous, T. (June 5, 2017). "Adaptive Control of Linear Time-Varying Interval Systems." ASME. J. Dyn. Sys., Meas., Control. September 2017; 139(9): 091006. https://doi.org/10.1115/1.4035927
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