H∞ control for nonlinear stochastic systems: The output-feedback case

Nadav Berman; Uri Shaked

doi:10.3182/20050703-6-cz-1902.00386

H_∞ control for nonlinear stochastic systems: The output-feedback case

Nadav Berman, Uri Shaked

Department of Mechanical Engineering

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

Abstract

in this paper we develop an H_∞ control theory, from the dissipation point of view, for a large class of time-continuous, stochastic, nonlinear, time-invariant systems with outputfeedback. in particular, we introduce a notion of stochastic dissipative systems, analogously to the familiar notion of dissipation associated with deterministic systems and we utilize it as a basis for the development of the theory. in particular, we utilize the stochastic version of what is called Bounded Real Lemma (BRL) to synthesize an output-feedback controller. It is shown that this controller makes the resulting closed-loop system dissipative. Stability, in probability and in the mean square sense, is discussed and sufficient conditions for achieving the stability and the H_∞ performance are introduced.

Original language	English
Title of host publication	Proceedings of the 16th IFAC World Congress, IFAC 2005
Publisher	IFAC Secretariat
Pages	200-205
Number of pages	6
ISBN (Print)	008045108X, 9780080451084
DOIs	https://doi.org/10.3182/20050703-6-cz-1902.00386
State	Published - 1 Jan 2005

Publication series

Name	IFAC Proceedings Volumes (IFAC-PapersOnline)
Volume	16
ISSN (Print)	1474-6670

Keywords

Disturbance attenuation
Nonlinear systems
Stochastic systems

ASJC Scopus subject areas

Control and Systems Engineering

Access to Document

10.3182/20050703-6-cz-1902.00386

Cite this

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title = "H∞ control for nonlinear stochastic systems: The output-feedback case",

abstract = "in this paper we develop an H∞ control theory, from the dissipation point of view, for a large class of time-continuous, stochastic, nonlinear, time-invariant systems with outputfeedback. in particular, we introduce a notion of stochastic dissipative systems, analogously to the familiar notion of dissipation associated with deterministic systems and we utilize it as a basis for the development of the theory. in particular, we utilize the stochastic version of what is called Bounded Real Lemma (BRL) to synthesize an output-feedback controller. It is shown that this controller makes the resulting closed-loop system dissipative. Stability, in probability and in the mean square sense, is discussed and sufficient conditions for achieving the stability and the H∞ performance are introduced.",

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AB - in this paper we develop an H∞ control theory, from the dissipation point of view, for a large class of time-continuous, stochastic, nonlinear, time-invariant systems with outputfeedback. in particular, we introduce a notion of stochastic dissipative systems, analogously to the familiar notion of dissipation associated with deterministic systems and we utilize it as a basis for the development of the theory. in particular, we utilize the stochastic version of what is called Bounded Real Lemma (BRL) to synthesize an output-feedback controller. It is shown that this controller makes the resulting closed-loop system dissipative. Stability, in probability and in the mean square sense, is discussed and sufficient conditions for achieving the stability and the H∞ performance are introduced.

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