Maximum principle of a class of nonlinear PDE systems

Garng Morton Huang, T. S. Tang

Research output: Contribution to conferencePaper

Abstract

In Banach spaces with either L2 or L norm, a generalized integral version of the maximum principle for a class of nonlinear distributed-parameter systems (DPSs) and a generalized cost functional is obtained, and its pointwise version is proved to be equivalent to this integral form with an additional assumption on controls. The Hamilton-Jacobi equation for the DPSs is also obtained. To illustrate the use of the theory, the maximum principle and the Hamilton-Jacobi equation are applied to the design of optimal open-loop and feedback controls for a two-dimensional, nonlinear, hyperbolic system. The open-loop optimal control law is obtained without introducing model linearization and truncation. In the space with L-type norm the optimal feedback control law structure is obtained from the open-loop result. Two approximations to the optimal feedback control are analyzed, and the approximate errors are estimated in terms of the initial state norm.

Original languageEnglish
Pages1725-1730
Number of pages6
Publication statusPublished - 1 Dec 1989
Externally publishedYes
EventProceedings of the 1989 American Control Conference - Pittsburgh, PA, USA
Duration: 21 Jun 198923 Jun 1989

Other

OtherProceedings of the 1989 American Control Conference
CityPittsburgh, PA, USA
Period21/6/8923/6/89

Fingerprint

Maximum principle
Feedback control
Nonlinear systems
Banach spaces
Linearization

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Huang, G. M., & Tang, T. S. (1989). Maximum principle of a class of nonlinear PDE systems. 1725-1730. Paper presented at Proceedings of the 1989 American Control Conference, Pittsburgh, PA, USA, .

Maximum principle of a class of nonlinear PDE systems. / Huang, Garng Morton; Tang, T. S.

1989. 1725-1730 Paper presented at Proceedings of the 1989 American Control Conference, Pittsburgh, PA, USA, .

Research output: Contribution to conferencePaper

Huang, GM & Tang, TS 1989, 'Maximum principle of a class of nonlinear PDE systems' Paper presented at Proceedings of the 1989 American Control Conference, Pittsburgh, PA, USA, 21/6/89 - 23/6/89, pp. 1725-1730.
Huang GM, Tang TS. Maximum principle of a class of nonlinear PDE systems. 1989. Paper presented at Proceedings of the 1989 American Control Conference, Pittsburgh, PA, USA, .
Huang, Garng Morton ; Tang, T. S. / Maximum principle of a class of nonlinear PDE systems. Paper presented at Proceedings of the 1989 American Control Conference, Pittsburgh, PA, USA, .6 p.
@conference{c1cc6548332f492b8c550878f9a7a388,
title = "Maximum principle of a class of nonlinear PDE systems",
abstract = "In Banach spaces with either L2 or L∞ norm, a generalized integral version of the maximum principle for a class of nonlinear distributed-parameter systems (DPSs) and a generalized cost functional is obtained, and its pointwise version is proved to be equivalent to this integral form with an additional assumption on controls. The Hamilton-Jacobi equation for the DPSs is also obtained. To illustrate the use of the theory, the maximum principle and the Hamilton-Jacobi equation are applied to the design of optimal open-loop and feedback controls for a two-dimensional, nonlinear, hyperbolic system. The open-loop optimal control law is obtained without introducing model linearization and truncation. In the space with L∞-type norm the optimal feedback control law structure is obtained from the open-loop result. Two approximations to the optimal feedback control are analyzed, and the approximate errors are estimated in terms of the initial state norm.",
author = "Huang, {Garng Morton} and Tang, {T. S.}",
year = "1989",
month = "12",
day = "1",
language = "English",
pages = "1725--1730",
note = "Proceedings of the 1989 American Control Conference ; Conference date: 21-06-1989 Through 23-06-1989",

}

TY - CONF

T1 - Maximum principle of a class of nonlinear PDE systems

AU - Huang, Garng Morton

AU - Tang, T. S.

PY - 1989/12/1

Y1 - 1989/12/1

N2 - In Banach spaces with either L2 or L∞ norm, a generalized integral version of the maximum principle for a class of nonlinear distributed-parameter systems (DPSs) and a generalized cost functional is obtained, and its pointwise version is proved to be equivalent to this integral form with an additional assumption on controls. The Hamilton-Jacobi equation for the DPSs is also obtained. To illustrate the use of the theory, the maximum principle and the Hamilton-Jacobi equation are applied to the design of optimal open-loop and feedback controls for a two-dimensional, nonlinear, hyperbolic system. The open-loop optimal control law is obtained without introducing model linearization and truncation. In the space with L∞-type norm the optimal feedback control law structure is obtained from the open-loop result. Two approximations to the optimal feedback control are analyzed, and the approximate errors are estimated in terms of the initial state norm.

AB - In Banach spaces with either L2 or L∞ norm, a generalized integral version of the maximum principle for a class of nonlinear distributed-parameter systems (DPSs) and a generalized cost functional is obtained, and its pointwise version is proved to be equivalent to this integral form with an additional assumption on controls. The Hamilton-Jacobi equation for the DPSs is also obtained. To illustrate the use of the theory, the maximum principle and the Hamilton-Jacobi equation are applied to the design of optimal open-loop and feedback controls for a two-dimensional, nonlinear, hyperbolic system. The open-loop optimal control law is obtained without introducing model linearization and truncation. In the space with L∞-type norm the optimal feedback control law structure is obtained from the open-loop result. Two approximations to the optimal feedback control are analyzed, and the approximate errors are estimated in terms of the initial state norm.

UR - http://www.scopus.com/inward/record.url?scp=0024902168&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0024902168&partnerID=8YFLogxK

M3 - Paper

SP - 1725

EP - 1730

ER -