H∞ and H2 optimal controllers for periodic and multi-rate systems

Petros G. Voulgaris; Munther A. Dahleh; Lena S. Valavani

H^∞ and H² optimal controllers for periodic and multi-rate systems

Petros G. Voulgaris
, Munther A. Dahleh
, Lena S. Valavani

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

Abstract

The solutions to the optimal l² to l² disturbance rejection problem (H^∞) as well as to the LQG (linear quadratic Gaussian) (H²) problem in periodic systems using the lifting technique are presented. Both problems involve a causality condition on the optimal LTI (linear time invariant) compensator when viewed in the lifted domain. The H^∞ problem is solved using the Nehari's theorem, whereas in the H² problem the solution is obtained using the projection theorem in Hilbert spaces. The authors demonstrate that exactly the same method of solution to the H^∞ and H² problems in periodic systems applies when considering the same problems in multirate sampled data systems.

Original language	English (US)
Title of host publication	Proceedings of the IEEE Conference on Decision and Control
Publisher	Publ by IEEE
Pages	214-216
Number of pages	3
ISBN (Print)	0780304500
State	Published - Jan 1992
Externally published	Yes
Event	Proceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3) - Brighton, Engl Duration: Dec 11 1991 → Dec 13 1991

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0191-2216

Other

Other	Proceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3)
City	Brighton, Engl
Period	12/11/91 → 12/13/91

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Library availability

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Cite this

H^∞ and H² optimal controllers for periodic and multi-rate systems. / Voulgaris, Petros G.; Dahleh, Munther A.; Valavani, Lena S.
Proceedings of the IEEE Conference on Decision and Control. Publ by IEEE, 1992. p. 214-216 (Proceedings of the IEEE Conference on Decision and Control).

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

Voulgaris, PG, Dahleh, MA & Valavani, LS 1992, H^∞ and H² optimal controllers for periodic and multi-rate systems. in Proceedings of the IEEE Conference on Decision and Control. Proceedings of the IEEE Conference on Decision and Control, Publ by IEEE, pp. 214-216, Proceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3), Brighton, Engl, 12/11/91.

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abstract = "The solutions to the optimal l2 to l2 disturbance rejection problem (H∞) as well as to the LQG (linear quadratic Gaussian) (H2) problem in periodic systems using the lifting technique are presented. Both problems involve a causality condition on the optimal LTI (linear time invariant) compensator when viewed in the lifted domain. The H∞ problem is solved using the Nehari's theorem, whereas in the H2 problem the solution is obtained using the projection theorem in Hilbert spaces. The authors demonstrate that exactly the same method of solution to the H∞ and H2 problems in periodic systems applies when considering the same problems in multirate sampled data systems.",

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note = "Acknowledgements--The first and third authors were supported by the AFOSR-Elgin A.F.B. under grant F08635-87-K-0031, by the NASA Ames and Langley Research Centers under grant NASA/NAG-2-297 and by a gift from the Boeing Corporation. The second author was supported by the Draper Laboratory grant DC-H-441636 and by NSF grant 9157306-ECS.; Proceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3) ; Conference date: 11-12-1991 Through 13-12-1991",

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N2 - The solutions to the optimal l2 to l2 disturbance rejection problem (H∞) as well as to the LQG (linear quadratic Gaussian) (H2) problem in periodic systems using the lifting technique are presented. Both problems involve a causality condition on the optimal LTI (linear time invariant) compensator when viewed in the lifted domain. The H∞ problem is solved using the Nehari's theorem, whereas in the H2 problem the solution is obtained using the projection theorem in Hilbert spaces. The authors demonstrate that exactly the same method of solution to the H∞ and H2 problems in periodic systems applies when considering the same problems in multirate sampled data systems.

AB - The solutions to the optimal l2 to l2 disturbance rejection problem (H∞) as well as to the LQG (linear quadratic Gaussian) (H2) problem in periodic systems using the lifting technique are presented. Both problems involve a causality condition on the optimal LTI (linear time invariant) compensator when viewed in the lifted domain. The H∞ problem is solved using the Nehari's theorem, whereas in the H2 problem the solution is obtained using the projection theorem in Hilbert spaces. The authors demonstrate that exactly the same method of solution to the H∞ and H2 problems in periodic systems applies when considering the same problems in multirate sampled data systems.

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