### 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 |

Externally published | Yes |

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 |

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### ASJC Scopus subject areas

- Engineering(all)

### 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, .

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

Research output: Contribution to conference › Paper

}

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.

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M3 - Paper

SP - 1725

EP - 1730

ER -