Relations between (Hl-)optimal control of a nonlinear system and its linearization

Arjan van der Schaft

doi:10.1109/CDC.1991.261720

Relations between (Hl-)optimal control of a nonlinear system and its linearization

Arjan van der Schaft

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

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Abstract

In a previous work (1991), the author showed some basic connections between H∞ control of a nonlinear control system and H¿ control of its linearization. A key argument was that the existence and parametrization, at least locally, of the stable invariant manifold of a certain Hamiltonian vector field are determined by the Hamiltonian matrix corresponding to the linearized problem. Using the same methodology, the author gives a quick proof of the fact that a nonlinear optimal control problem is locally solvable if the associated LQ problem is solvable. This was proved before by D.L. Lukes (1969) under much stronger conditions

Original language	Undefined
Title of host publication	30th IEEE CDC
Place of Publication	Brighton, U.K.
Publisher	IEEE
Pages	1807-1808
Number of pages	2
DOIs	https://doi.org/10.1109/CDC.1991.261720
Publication status	Published - 11 Dec 1991
Event	30th IEEE Conference on Decision and Control, CDC 1991 - Brighton, United Kingdom Duration: 11 Dec 1991 → 13 Dec 1991 Conference number: 30

Publication series

Name
Publisher	IEEE
Volume	2

Conference

Conference	30th IEEE Conference on Decision and Control, CDC 1991
Abbreviated title	CDC
Country/Territory	United Kingdom
City	Brighton
Period	11/12/91 → 13/12/91

Keywords

IR-30933
METIS-141574

Access to Document

10.1109/CDC.1991.261720

00261720

Cite this

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title = "Relations between (Hl-)optimal control of a nonlinear system and its linearization",

abstract = "In a previous work (1991), the author showed some basic connections between H∞ control of a nonlinear control system and H¿ control of its linearization. A key argument was that the existence and parametrization, at least locally, of the stable invariant manifold of a certain Hamiltonian vector field are determined by the Hamiltonian matrix corresponding to the linearized problem. Using the same methodology, the author gives a quick proof of the fact that a nonlinear optimal control problem is locally solvable if the associated LQ problem is solvable. This was proved before by D.L. Lukes (1969) under much stronger conditions",

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N2 - In a previous work (1991), the author showed some basic connections between H∞ control of a nonlinear control system and H¿ control of its linearization. A key argument was that the existence and parametrization, at least locally, of the stable invariant manifold of a certain Hamiltonian vector field are determined by the Hamiltonian matrix corresponding to the linearized problem. Using the same methodology, the author gives a quick proof of the fact that a nonlinear optimal control problem is locally solvable if the associated LQ problem is solvable. This was proved before by D.L. Lukes (1969) under much stronger conditions

AB - In a previous work (1991), the author showed some basic connections between H∞ control of a nonlinear control system and H¿ control of its linearization. A key argument was that the existence and parametrization, at least locally, of the stable invariant manifold of a certain Hamiltonian vector field are determined by the Hamiltonian matrix corresponding to the linearized problem. Using the same methodology, the author gives a quick proof of the fact that a nonlinear optimal control problem is locally solvable if the associated LQ problem is solvable. This was proved before by D.L. Lukes (1969) under much stronger conditions

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Y2 - 11 December 1991 through 13 December 1991

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