Robust adaptive stabilization with multiple H∞ uncertainty models and switching

Sundeep Rangan; Kameshwar Poolla

doi:10.1109/ACC.1998.703293

Robust adaptive stabilization with multiple H_∞ uncertainty models and switching

Sundeep Rangan, Kameshwar Poolla

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

In this paper, we consider a simple robust adaptive stabilization problem based on an H_∞ uncertainty model with a discrete unknown parameter. In the proposed problem formulation, the unknown plant is assumed to belong to one of N possible uncertainty models, where each model is described by a known, linear nominal plant with H_∞ bounds on the unmodeled dynamics. We show that if each of the models can be robustly stabilized with a linear time-invariant (LTI) controller, then there exists a single adaptive (possibly nonlinear and time-varying) controller that simultaneously robustly stabilizes all the N possible uncertainty models. The adaptive controller can provide the same level of stability robustness as the LTI controllers, and introduces, at most, a bounded transient in the output. Our approach is based on a simple switching algorithm and a novel application of H_∞ filtering methods.

Original language	English (US)
Title of host publication	Proceedings of the 1998 American Control Conference, ACC 1998
Pages	3644-3648
Number of pages	5
DOIs	https://doi.org/10.1109/ACC.1998.703293
State	Published - 1998
Event	1998 American Control Conference, ACC 1998 - Philadelphia, PA, United States Duration: Jun 24 1998 → Jun 26 1998

Publication series

Name	Proceedings of the American Control Conference
Volume	6
ISSN (Print)	0743-1619

Other

Other	1998 American Control Conference, ACC 1998
Country/Territory	United States
City	Philadelphia, PA
Period	6/24/98 → 6/26/98

ASJC Scopus subject areas

Electrical and Electronic Engineering

Access to Document

10.1109/ACC.1998.703293

Cite this

Rangan, S & Poolla, K 1998, Robust adaptive stabilization with multiple H_∞ uncertainty models and switching. in Proceedings of the 1998 American Control Conference, ACC 1998., 703293, Proceedings of the American Control Conference, vol. 6, pp. 3644-3648, 1998 American Control Conference, ACC 1998, Philadelphia, PA, United States, 6/24/98. https://doi.org/10.1109/ACC.1998.703293

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abstract = "In this paper, we consider a simple robust adaptive stabilization problem based on an H∞ uncertainty model with a discrete unknown parameter. In the proposed problem formulation, the unknown plant is assumed to belong to one of N possible uncertainty models, where each model is described by a known, linear nominal plant with H∞ bounds on the unmodeled dynamics. We show that if each of the models can be robustly stabilized with a linear time-invariant (LTI) controller, then there exists a single adaptive (possibly nonlinear and time-varying) controller that simultaneously robustly stabilizes all the N possible uncertainty models. The adaptive controller can provide the same level of stability robustness as the LTI controllers, and introduces, at most, a bounded transient in the output. Our approach is based on a simple switching algorithm and a novel application of H∞ filtering methods.",

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