Feedback stabilization of the nonlinear pendulum under uncertainty: A robustness issue
type: Item
instance of: scholarly article
title: Feedback stabilization of the nonlinear pendulum under uncertainty: A robustness issue
zbMATH Open document ID: 0588.93057
DOI: 10.1016/0167-6911(86)90115-5
author: Fathi M. A. Salam
published in: Systems \& Control Letters
publication date: 1986-01-01T00:00:00Z
review text: We examine the control of a (prototype) nonlinear pendulum under uncertainty in modelling. The uncertainty is sufficiently small and is a function of both state and time. We apply Liapunov's direct method to prove the stability of an equilibrium point. Then, we apply Melnikov's method to introduce a criterion for the control to avoid deforming the actual region of stability of the equilibrium point. We demonstrate the cooperative relationship between the Liapunov and Melnikov methods in assessing stability. Consequently, we propose preserving the size and shape of the region of stability, and preventing the creation of complicated dynamics on its boundary, as indicative of robust control. In essence, robustness of controllers for nonlinear systems must be treated from (nonlocal) dynamical systems viewpoint. A simulation result is given which quantitatively supports the analysis.
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 70K20
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 93B35
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 93D20
zbMATH DE Number: 3946012
zbMATH Keywords: nonlinear pendulum
zbMATH Keywords: uncertainty
zbMATH Keywords: Liapunov's direct method
zbMATH Keywords: Melnikov's method
zbMATH Keywords: region of stability
zbMATH Keywords: robust control
MaRDI profile type: Publication
full work available at URL: 0167-6911(86)90115-5
OpenAlex ID: W2022433032
cites work: Q5582924
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description: scientific article; zbMATH DE number 3946012