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

A.J. van der Schaft

doi:10.1109/CDC.1993.325164

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

A.J. van der Schaft

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

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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 language	English
Title of host publication	Proceedings of the 32nd IEEE Conference on Decision and Control
Subtitle of host publication	December 15-17, 1993, Marriott Rivercenter, San Antonio, Texas, USA
Place of Publication	Piscataway, NJ, USA
Publisher	IEEE
Pages	202-203
Number of pages	2
ISBN (Print)	9780780312982
DOIs	https://doi.org/10.1109/CDC.1993.325164
Publication status	Published - 1 Jun 1993
Event	32nd IEEE Conference on Decision and Control, CDC 1993 - San Antonio, United States Duration: 15 Dec 1993 → 17 Dec 1993 Conference number: 32

Publication series

Name	Proceedings IEEE Conference on Decision and Control (CDC)
Publisher	IEEE
ISSN (Print)	0191-2216

Conference

Conference	32nd IEEE Conference on Decision and Control, CDC 1993
Abbreviated title	CDC
Country	United States
City	San Antonio
Period	15/12/93 → 17/12/93

Access to Document

10.1109/CDC.1993.325164

VanderSchaft1993nonlinear
open
Final published version, 219 KB

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van der Schaft, A. J. (1993). Nonlinear systems which have finite-dimensional H-infinity suboptimal central controllers. In Proceedings of the 32nd IEEE Conference on Decision and Control: December 15-17, 1993, Marriott Rivercenter, San Antonio, Texas, USA (pp. 202-203). (Proceedings IEEE Conference on Decision and Control (CDC)). IEEE. https://doi.org/10.1109/CDC.1993.325164

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title = "Nonlinear systems which have finite-dimensional H-infinity suboptimal central controllers",

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).",

author = "{van der Schaft}, A.J.",

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van der Schaft, AJ 1993, Nonlinear systems which have finite-dimensional H-infinity suboptimal central controllers. in Proceedings of the 32nd IEEE Conference on Decision and Control: December 15-17, 1993, Marriott Rivercenter, San Antonio, Texas, USA. Proceedings IEEE Conference on Decision and Control (CDC), IEEE, Piscataway, NJ, USA, pp. 202-203, 32nd IEEE Conference on Decision and Control, CDC 1993, San Antonio, United States, 15/12/93. https://doi.org/10.1109/CDC.1993.325164

Nonlinear systems which have finite-dimensional H-infinity suboptimal central controllers. / van der Schaft, A.J.

Proceedings of the 32nd IEEE Conference on Decision and Control: December 15-17, 1993, Marriott Rivercenter, San Antonio, Texas, USA. Piscataway, NJ, USA : IEEE, 1993. p. 202-203 (Proceedings IEEE Conference on Decision and Control (CDC)).

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

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N2 - 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).

AB - 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).

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van der Schaft AJ. Nonlinear systems which have finite-dimensional H-infinity suboptimal central controllers. In Proceedings of the 32nd IEEE Conference on Decision and Control: December 15-17, 1993, Marriott Rivercenter, San Antonio, Texas, USA. Piscataway, NJ, USA: IEEE. 1993. p. 202-203. (Proceedings IEEE Conference on Decision and Control (CDC)). https://doi.org/10.1109/CDC.1993.325164