Unified approach to H-optimal control of singularly perturbed systems: Imperfect state measurements

H. Singh, R. H. Brown, D. S. Naidu

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

The key contribution of the current paper is to present continuous-time and discrete-time singularly perturbed cases simultaneously under general imperfect state measurements using infinite-horizon formulations from the game theoretic approach, thereby highlighting the similarities and differences. We first show that as the small parameter ε approaches zero, the optimal disturbance attenuation levels for a full order system under a quadratic performance index converges to the maximum of the optimal disturbance attenuation levels for the slow and fast subsystems under appropriate slow and fast quadratic cost functions. Then, we construct a controller based on the slow subsystem only, and obtain conditions under which it delivers a desired performance level even though the fast dynamics have been completely neglected. The ultimate performance level achieved by this `slow' controller can be uniformly improved upon, however, by a composite controller that uses some feedback from the output of the fast subsystem. We construct one such controller via a two step sequential procedure that uses static feedback from the fast system output and dynamic feedback from an appropriate slow system output, each one obtained by solving appropriate ε-independent lower dimensional H-optimal control problems under some informational constraints.

Original languageEnglish (US)
Pages (from-to)2909-2913
Number of pages5
JournalProceedings of the American Control Conference
Volume4
StatePublished - Dec 1 1999

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