G-RKHS of bounded nonlinear operators for nonlinear systems control
Research output: Journal Publications and Reviews › RGC 22 - Publication in policy or professional journal
Author(s)
Detail(s)
Original language | English |
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Pages (from-to) | 96-101 |
Journal / Publication | Proceedings of the IEEE Conference on Decision and Control |
Volume | 1 |
Publication status | Published - 1989 |
Externally published | Yes |
Conference
Title | Proceedings of the 28th IEEE Conference on Decision and Control. Part 1 (of 3) |
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City | Tampa, FL, USA |
Period | 13 - 15 December 1989 |
Link(s)
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.
Citation Format(s)
G-RKHS of bounded nonlinear operators for nonlinear systems control. / Chen, Guanrong; de Figueiredo, Rui J P.
In: Proceedings of the IEEE Conference on Decision and Control, Vol. 1, 1989, p. 96-101.
In: Proceedings of the IEEE Conference on Decision and Control, Vol. 1, 1989, p. 96-101.
Research output: Journal Publications and Reviews › RGC 22 - Publication in policy or professional journal