Maximum principle of a class of nonlinear PDE systems

G. 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
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

ASJC Scopus subject areas

  • Engineering(all)

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    Huang, G., & 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, .