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Relations between (H∞) optimal control of a nonlinear system and its linearization

Schaft, A. J. V. D., 1991, Proceedings of the 30th IEEE Conference on Decision and Control. University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science, p. 1807-1808 2 p.

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In a previous paper we 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 is determined by the Hamiltonian matrix corresponding to the linearized problem. Using the same methodology we are able to give 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 under much stronger conditions.
Original languageEnglish
Title of host publicationProceedings of the 30th IEEE Conference on Decision and Control
PublisherUniversity of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science
Pages1807-1808
Number of pages2
ISBN (Print)0780304500
Publication statusPublished - 1991

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