Near-optimal feedback stabilization of a class of nonlinear singularly perturbed systems

Chow, Joe H.; Kokotović, P.V.

doi:10.1109/cdc.1978.267942

Cited by 2 publications

(4 citation statements)

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“…We assume further The subscripts of L* correspond to the third and irl = Fl(Vl), (3)(4)(5)(6)(7)(8)(9) the fourth varliables in the system of (2.3). To avoid cumbersome notation we shall omit E argument in the functions below.…”

Section: Resultsmentioning

confidence: 99%

“…Nonlinear optimal control problem for singularly perturbed systems leads to a high dimensional Hamilton-Jacobi partial differential equation of twotime-scales for an optimal controller evaluation [3].…”

Section: Introductionmentioning

confidence: 99%

“…To alleviate the di:Eculties caused by the high dimensionality and t:he stiffness that result from the interaction of slow and fast dynamical modes, a composite control1e:r was designed [3], [6]. This Eindependent controller was based on the reducedorder slow and fast subproblems.…”

Section: Introductionmentioning

confidence: 99%

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

Fridman

1998

Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207)

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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 Hamiltonian system. We obtain exact slow-fast decomposition of the Hamiltonian system and of the special invariant manifold into the slow and the fast ones. We get sufficient conditions for the solvability of the HamiltonJacobi 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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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Fridman

1998

Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207)

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“…In fact, the fast nature of the observer used in equation (20), which allows treatment of the closed-loop system within the singular perturbations framework, makes such an extension quite natural without the need to impose any additional restrictive assumptions. For some related results on near-optimal control of singularly perturbed systems, the reader is referred to Chow and Kokotovic (1978) and Fridman (1996Fridman ( , 1998.…”

Section: Remarkmentioning

confidence: 99%

Robust near-optimal output feedback control of non-linear systems

El‐Farra

Christofides

2001

International Journal of Control

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Near-optimal feedback stabilization of a class of nonlinear singularly perturbed systems

Cited by 2 publications

References 5 publications

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

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

Robust near-optimal output feedback control of non-linear systems

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