Nonlinear systems which have finite-dimensional H-infinity suboptimal central controllers

A.J. van der Schaft

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    Abstract

    Following the work of Basar and Bernhard (1990), the authors derived (1993) the nonlinear central controller solving the nonlinear (standard) H∞ suboptimal control problem. This nonlinear central controller is an infinite-dimensional system, and resembles very much the solution in nonlinear stochastic filtering or nonlinear deterministic filtering. After showing that in the linear case the nonlinear central controller reduces to the finite-dimensional central controller, we consider in the present note the question if there are truly nonlinear systems having finite-dimensional central controllers. Guided by similar considerations in nonlinear stochastic and deterministic filtering, we characterize a specific class of nonlinear systems having finite-dimensional central controllers. This class can be regarded as the deterministic H∞ analogue of the class of nonlinear systems admitting finite dimensional filters as identified by Benes (1981).
    Original languageEnglish
    Title of host publicationProceedings of the 32nd IEEE Conference on Decision and Control
    Subtitle of host publicationDecember 15-17, 1993, Marriott Rivercenter, San Antonio, Texas, USA
    Place of PublicationPiscataway, NJ, USA
    PublisherIEEE
    Pages202-203
    Number of pages2
    ISBN (Print)9780780312982
    DOIs
    Publication statusPublished - 1 Jun 1993
    Event32nd IEEE Conference on Decision and Control, CDC 1993 - San Antonio, United States
    Duration: 15 Dec 199317 Dec 1993
    Conference number: 32

    Publication series

    NameProceedings IEEE Conference on Decision and Control (CDC)
    PublisherIEEE
    ISSN (Print)0191-2216

    Conference

    Conference32nd IEEE Conference on Decision and Control, CDC 1993
    Abbreviated titleCDC
    CountryUnited States
    CitySan Antonio
    Period15/12/9317/12/93

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