Maximum principle of a class of nonlinear PDE systems

G. Huang, T. S. Tang

Research output: Contribution to conferencePaper


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
Number of pages6
Publication statusPublished - 1 Dec 1989
EventProceedings of the 1989 American Control Conference - Pittsburgh, PA, USA
Duration: 21 Jun 198923 Jun 1989


OtherProceedings of the 1989 American Control Conference
CityPittsburgh, PA, USA

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, .