H∞-optimal control for singularly perturbed systems. Part I: Perfect state measurements

Zigang Pan, M Tamer Basar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study the H-optimal control of singularly perturbed linear systems under perfect state measurements. Using a differential game theoretic approach, we show that as the singular perturbation parameter ε approaches zero, the optimal disturbance attenuation level for the full-order system under a quadratic performance index converges to a value that is bounded above by the maximum of the optimal disturbance attenuation levels for the slow and fast subsystems under appropriate 'slow' and 'fast' quadratic cost functions. Furthermore, we construct a composite controller based on the solution of the slow and fast games, which guarantees a desired achievable performance level for the full-order plant, as ε approaches zero. A 'slow' controller, however, is not generally robust in this sense, but still under some conditions, which are delineated in the paper, the fast dynamics can be totally ignored. The paper also studies optimality when the controller includes a feedforward term in the disturbance.

Original languageEnglish (US)
Title of host publicationProceedings of the American Control Conference
PublisherPubl by American Automatic Control Council
Pages1850-1854
Number of pages5
ISBN (Print)0780302109
StatePublished - Dec 1 1992
EventProceedings of the 1992 American Control Conference - Chicago, IL, USA
Duration: Jun 24 1992Jun 26 1992

Publication series

NameProceedings of the American Control Conference
Volume3
ISSN (Print)0743-1619

Other

OtherProceedings of the 1992 American Control Conference
CityChicago, IL, USA
Period6/24/926/26/92

Fingerprint

Controllers
Cost functions
Linear systems
Composite materials

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Pan, Z., & Basar, M. T. (1992). H∞-optimal control for singularly perturbed systems. Part I: Perfect state measurements. In Proceedings of the American Control Conference (pp. 1850-1854). (Proceedings of the American Control Conference; Vol. 3). Publ by American Automatic Control Council.

H∞-optimal control for singularly perturbed systems. Part I : Perfect state measurements. / Pan, Zigang; Basar, M Tamer.

Proceedings of the American Control Conference. Publ by American Automatic Control Council, 1992. p. 1850-1854 (Proceedings of the American Control Conference; Vol. 3).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Pan, Z & Basar, MT 1992, H∞-optimal control for singularly perturbed systems. Part I: Perfect state measurements. in Proceedings of the American Control Conference. Proceedings of the American Control Conference, vol. 3, Publ by American Automatic Control Council, pp. 1850-1854, Proceedings of the 1992 American Control Conference, Chicago, IL, USA, 6/24/92.
Pan Z, Basar MT. H∞-optimal control for singularly perturbed systems. Part I: Perfect state measurements. In Proceedings of the American Control Conference. Publ by American Automatic Control Council. 1992. p. 1850-1854. (Proceedings of the American Control Conference).
Pan, Zigang ; Basar, M Tamer. / H∞-optimal control for singularly perturbed systems. Part I : Perfect state measurements. Proceedings of the American Control Conference. Publ by American Automatic Control Council, 1992. pp. 1850-1854 (Proceedings of the American Control Conference).
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