Hybrid H∞ control Based on multiple Lyapunov functions

Jun Zhao; David J. Hill

doi:10.1016/S1474-6670(17)31260-0

Hybrid H^∞ control Based on multiple Lyapunov functions

Jun Zhao
, David J. Hill

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

1 Citation (Scopus)

Abstract

The problem of H^∞ control for switched nonlinear systems is addressed in this paper. Based on multiple Lyapunov functions, a sufficient condition for the problem to be solvable is derived in terms of partial differential inequalities. This condition is a generalization of the well known Hamilton-Jacobi inequalities for the nonlinear H^∞ control problem. The continuous controllers for each subsystem and the switching law are simultaneously designed. As a direct application, a hybrid slate feedback strategy is proposed to solve the standard H^∞ control problem for nonlinear systems when no single continuous controller is effective.

Original language	English
Title of host publication	6th IFAC Symposium on Nonlinear Control Systems 2004 (NOLCOS 2004), Stuttgart, Germany, 1-3 September, 2004
Publisher	Elsevier
Pages	423-428
Number of pages	6
Volume	37
Edition	13
DOIs	https://doi.org/10.1016/S1474-6670(17)31260-0
Publication status	Published - 2004
Externally published	Yes
Event	IFAC Symposium on Nonlinear Control Systems 2004 - Stuttgart, Germany Duration: 1 Sept 2004 → 3 Sept 2004 Conference number: 6th https://www.sciencedirect.com/journal/ifac-proceedings-volumes/vol/37/issue/13

Publication series

Name	IFAC Proceedings Volumes (IFAC-PapersOnline)
Publisher	Elsevier - International Federation of Automatic Control (IFAC)
ISSN (Print)	1474-6670

Conference

Conference	IFAC Symposium on Nonlinear Control Systems 2004
Abbreviated title	NOLCOS 2004
Country/Territory	Germany
City	Stuttgart
Period	1/09/04 → 3/09/04
Internet address	https://www.sciencedirect.com/journal/ifac-proceedings-volumes/vol/37/issue/13

Keywords

H control
Hamilton-j acobi inequalities
Multiple Lyapunov functions
Switched systems

Access to Document

10.1016/S1474-6670(17)31260-0

Cite this

@inproceedings{30aec380af4d4f05bf50941a725ae751,

title = "Hybrid H∞ control Based on multiple Lyapunov functions",

abstract = "The problem of H∞ control for switched nonlinear systems is addressed in this paper. Based on multiple Lyapunov functions, a sufficient condition for the problem to be solvable is derived in terms of partial differential inequalities. This condition is a generalization of the well known Hamilton-Jacobi inequalities for the nonlinear H∞ control problem. The continuous controllers for each subsystem and the switching law are simultaneously designed. As a direct application, a hybrid slate feedback strategy is proposed to solve the standard H∞ control problem for nonlinear systems when no single continuous controller is effective.",

keywords = "H control, Hamilton-j acobi inequalities, Multiple Lyapunov functions, Switched systems",

author = "Jun Zhao and Hill, \{David J.\}",

note = "Funding Information: 1 supported by the Hong Kong Research Grants Council under Grant No.9040723 {"}Global Control of Complex Systems{"}, and NSF of China under Grant No.60274009 Publisher Copyright: Copyright {\textcopyright} 2004 IFAC.; IFAC Symposium on Nonlinear Control Systems 2004, NOLCOS 2004 ; Conference date: 01-09-2004 Through 03-09-2004",

year = "2004",

doi = "10.1016/S1474-6670(17)31260-0",

language = "English",

volume = "37",

series = "IFAC Proceedings Volumes (IFAC-PapersOnline)",

publisher = "Elsevier",

pages = "423--428",

booktitle = "6th IFAC Symposium on Nonlinear Control Systems 2004 (NOLCOS 2004), Stuttgart, Germany, 1-3 September, 2004",

address = "Netherlands",

edition = "13",

url = "https://www.sciencedirect.com/journal/ifac-proceedings-volumes/vol/37/issue/13",

}

Zhao, J & Hill, DJ 2004, Hybrid H^∞ control Based on multiple Lyapunov functions. in 6th IFAC Symposium on Nonlinear Control Systems 2004 (NOLCOS 2004), Stuttgart, Germany, 1-3 September, 2004. 13 edn, vol. 37, IFAC Proceedings Volumes (IFAC-PapersOnline), Elsevier, pp. 423-428, IFAC Symposium on Nonlinear Control Systems 2004, Stuttgart, Germany, 1/09/04. https://doi.org/10.1016/S1474-6670(17)31260-0

Hybrid H^∞ control Based on multiple Lyapunov functions. / Zhao, Jun; Hill, David J.
6th IFAC Symposium on Nonlinear Control Systems 2004 (NOLCOS 2004), Stuttgart, Germany, 1-3 September, 2004. Vol. 37 13. ed. Elsevier, 2004. p. 423-428 (IFAC Proceedings Volumes (IFAC-PapersOnline)).

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

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AU - Hill, David J.

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AB - The problem of H∞ control for switched nonlinear systems is addressed in this paper. Based on multiple Lyapunov functions, a sufficient condition for the problem to be solvable is derived in terms of partial differential inequalities. This condition is a generalization of the well known Hamilton-Jacobi inequalities for the nonlinear H∞ control problem. The continuous controllers for each subsystem and the switching law are simultaneously designed. As a direct application, a hybrid slate feedback strategy is proposed to solve the standard H∞ control problem for nonlinear systems when no single continuous controller is effective.

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KW - Hamilton-j acobi inequalities

KW - Multiple Lyapunov functions

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