Journal article

Publication year: 2020

Pages: 467-491

Journal: Acta cybernetica

Volume number: 24

Issue number: 3

ISSN: 0324-721X

Open access status: Gold

DOI Link: https://doi.org/10.14232/actacyb.24.3.2020.11

Publisher: Universitas Szegediensis

Abstract: 
In real-life applications, dynamic systems are often subject to uncertainty due to model simplifications, measurement inaccuracy or approximation errors which can be mapped to specific parameters. Uncertainty in dynamic systems can come either in stochastic forms or as interval representations. The latter is applied if the uncertainty is bounded as it will be done in this paper. The main idea is to find a joint approach for an interval-based gain scheduling controller while simultaneously reducing overestimation by enclosing state intervals with the least amount of conservativity. The robust and/ or optimal control design is realized using linear matrix inequalities (LMIs) to find an efficient solution and aims at a guaranteed stabilization of the system dynamics over a predefined time horizon. A temporal reduction of the widths of intervals representing worst-case bounds of the system states at a specific point of time should occur due to asymptotic stability proven by the employed LMI-based design. However, for commonly used approaches in the computation of interval enclosures, those interval widths seemingly blow up due to the wrapping effect in many cases. To avoid this, we provide two interval enclosure techniques - an exploitation of cooperativity and an exponential approach - and discuss their applicability taking into account two real-life applications, a high-bay rack feeder and an inverse pendulum.

Harvard Citation style: Kersten, J., Rauh, A. and Asehemann, H. (2020) Verified Interval Enclosure Techniques for Robust Gain Scheduling Controllers, Acta cybernetica, 24(3), pp. 467-491. https://doi.org/10.14232/actacyb.24.3.2020.11

APA Citation style: Kersten, J., Rauh, A., & Asehemann, H. (2020). Verified Interval Enclosure Techniques for Robust Gain Scheduling Controllers. Acta cybernetica. 24(3), 467-491. https://doi.org/10.14232/actacyb.24.3.2020.11