### Abstract

In Banach spaces with either L^{2} 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 language | English |
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Pages | 1725-1730 |

Number of pages | 6 |

Publication status | Published - 1 Dec 1989 |

Event | Proceedings of the 1989 American Control Conference - Pittsburgh, PA, USA Duration: 21 Jun 1989 → 23 Jun 1989 |

### Other

Other | Proceedings of the 1989 American Control Conference |
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City | Pittsburgh, PA, USA |

Period | 21/6/89 → 23/6/89 |

### ASJC Scopus subject areas

- Engineering(all)

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## Cite this

*Maximum principle of a class of nonlinear PDE systems*. 1725-1730. Paper presented at Proceedings of the 1989 American Control Conference, Pittsburgh, PA, USA, .