G-RKHS of bounded nonlinear operators for nonlinear systems control

Research output: Journal Publications and ReviewsRGC 22 - Publication in policy or professional journal

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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)96-101
Journal / PublicationProceedings of the IEEE Conference on Decision and Control
Volume1
Publication statusPublished - 1989
Externally publishedYes

Conference

TitleProceedings of the 28th IEEE Conference on Decision and Control. Part 1 (of 3)
CityTampa, FL, USA
Period13 - 15 December 1989

Abstract

A generalized reproducing kernel Hilbert space (G-RKHS) of nonlinear Lipschitz operators is constructed for systems and control engineering applications. Specifically, the uniform topology is first introduced into the totality of one-parameter families of nonlinear Lipschitz operators to form a uniformly normed linear space, and then a generalized Bochner integral is introduced to define an operator-valued inner product structure and an induced norm for the space. It is shown that any closed and separable subspace of the resultant inner product space is a G-RKHS, which is a new mathematical structure. A generalized Fock space for the specific family of bounded nonlinear Volterra operators for multi-input/multi-output (MIMO) control systems can be constructed in the same manner. An application of the approach to a feedback design problem involving optimal disturbance rejection for general nonlinear MIMO control systems formulated in a Banach space setting is indicated.