TY - GEN

T1 - Exact slow-fast decomposition of the Hamilton-Jacobi equation of singularly perturbed systems

AU - Fridman, E.

PY - 1998

Y1 - 1998

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.

UR - http://www.scopus.com/inward/record.url?scp=0010651011&partnerID=8YFLogxK

U2 - 10.1109/ACC.1998.707226

DO - 10.1109/ACC.1998.707226

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AN - SCOPUS:0010651011

SN - 0780345304

SN - 9780780345300

T3 - Proceedings of the American Control Conference

SP - 1503

EP - 1507

BT - Proceedings of the 1998 American Control Conference, ACC 1998

T2 - 1998 American Control Conference, ACC 1998

Y2 - 24 June 1998 through 26 June 1998

ER -