Periodic Adaptive Stabilization of Rapidly Time-Varying Linear Systems
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Date
2019-06-19
Authors
Simard, Joel D.
Nielsen, Christopher
Miller, Daniel E.
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Abstract
Adaptive control deals with systems that have unknown and/or time-varying parameters. Most techniques are proven for the case in which any time variation is slow, with results for systems with fast time variations limited to those for which the time variation is of a known form or for which the plant has stable zero dynamics. In this paper, a new adaptive controller design methodology is proposed in which the time variation can be rapid and the plant may have unstable zero dynamics. Under the structural assumptions that the plant is relative degree one and that the plant uncertainty is a single scalar variable, as well as some mild regularity assumptions, it is proven that the closed-loop system is exponentially stable under fast parameter variations with persistent jumps. The proposed controller is nonlinear and periodic, and in each period the parameter is estimated and an appropriate stabilizing control signal is applied.
Description
This is a post-peer-review, pre-copyedit version of an article published in Mathematics of Control, Signals, and Systems. The final authenticated version is available online at: http://dx.doi.org/https://doi.org/10.1007/s00498-019-0236-6
Keywords
Adaptive control, gain scheduling control, time-varying plant, periodic control