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

E. Fridman

doi:10.1109/ACC.1998.707226

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

E. Fridman^*

^*Corresponding author for this work

School of Electrical Engineering

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

1 Scopus citations

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 language	English
Title of host publication	Proceedings of the 1998 American Control Conference, ACC 1998
Pages	1503-1507
Number of pages	5
DOIs	https://doi.org/10.1109/ACC.1998.707226
State	Published - 1998
Event	1998 American Control Conference, ACC 1998 - Philadelphia, PA, United States Duration: 24 Jun 1998 → 26 Jun 1998

Publication series

Name	Proceedings of the American Control Conference
Volume	3
ISSN (Print)	0743-1619

Conference

Conference	1998 American Control Conference, ACC 1998
Country/Territory	United States
City	Philadelphia, PA
Period	24/06/98 → 26/06/98

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10.1109/ACC.1998.707226

Cite this

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title = "Exact slow-fast decomposition of the Hamilton-Jacobi equation of singularly perturbed systems",

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.",

author = "E. Fridman",

year = "1998",

doi = "10.1109/ACC.1998.707226",

language = "אנגלית",

isbn = "0780345304",

series = "Proceedings of the American Control Conference",

pages = "1503--1507",

booktitle = "Proceedings of the 1998 American Control Conference, ACC 1998",

note = "1998 American Control Conference, ACC 1998 ; Conference date: 24-06-1998 Through 26-06-1998",

}

Fridman, E 1998, Exact slow-fast decomposition of the Hamilton-Jacobi equation of singularly perturbed systems. in Proceedings of the 1998 American Control Conference, ACC 1998., 707226, Proceedings of the American Control Conference, vol. 3, pp. 1503-1507, 1998 American Control Conference, ACC 1998, Philadelphia, PA, United States, 24/06/98. https://doi.org/10.1109/ACC.1998.707226

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N2 - 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.

AB - 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.

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T2 - 1998 American Control Conference, ACC 1998

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

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