Exact slow-fast decomposition of the Hamilton-Jacobi equation of singularly perturbed systems

E. Fridman*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We study a Hamilton-Jacobi partial differential equation, arizing in optimal control problem for an affine nonlinear singularly perturbed system. This equation is solvable iff there exists a special invariant manifold of the corresponding Harniltonian system. We obtain exact slow-fast decomposition of the Harniltonian system and of the special invariant manifold into the slow and the fast ones. We get sufficient conditions for the solvability of the Hamilton-Jacobi equation in terms of the reduced-order slow submanifold, or in the hyperbolic case, in terms of a reduced-order slow Riccati equation. On the basis of this decomposition we construct asymptotic expansions of the optimal state-feedback, optimal trajectory and optimal open-loop control in the powers of a small parameter.

Original languageEnglish
Title of host publicationProceedings of the 1998 American Control Conference, ACC 1998
Pages1503-1507
Number of pages5
DOIs
StatePublished - 1998
Event1998 American Control Conference, ACC 1998 - Philadelphia, PA, United States
Duration: 24 Jun 199826 Jun 1998

Publication series

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

Conference

Conference1998 American Control Conference, ACC 1998
Country/TerritoryUnited States
CityPhiladelphia, PA
Period24/06/9826/06/98

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