### Abstract

We generalize the standard H^{∞} control problem to the finite horizon case with two (possibly singular) terminal penalties at the initial and final times. The major objective of the generalization is to increase flexibility of IF controls. Transients in the finite horizon and the terminal penalties are taken into account within the framework of H^{∞} control problems. We give a complete solution, a necessary and sufficient condition, and a parameterization to the finite horizon H^{∞} control problem. The solution is a natural extension of the “Riccati equation” solution. In the special case, when all the terminal penalties vanish, the solution is reduced to the existing one and to the finite horizon standard H^{∞} control problem. Our approach to the problem is based on completing the square argument of a particular quadratic form, which is at least technically different from the previous ones.

Original language | English |
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Pages (from-to) | 1762-1767 |

Number of pages | 6 |

Journal | IEEE Transactions on Automatic Control |

Volume | 37 |

Issue number | 11 |

DOIs | |

Publication status | Published - 1992 |

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### ASJC Scopus subject areas

- Computer Science Applications
- Control and Systems Engineering
- Electrical and Electronic Engineering

### Cite this

^{∞}Control Problems with Terminal Penalties.

*IEEE Transactions on Automatic Control*,

*37*(11), 1762-1767. https://doi.org/10.1109/9.173146

**Finite Horizon H ^{∞} Control Problems with Terminal Penalties.** / Uchida, Kenko; Fujita, Masayuki.

Research output: Contribution to journal › Article

^{∞}Control Problems with Terminal Penalties',

*IEEE Transactions on Automatic Control*, vol. 37, no. 11, pp. 1762-1767. https://doi.org/10.1109/9.173146

^{∞}Control Problems with Terminal Penalties. IEEE Transactions on Automatic Control. 1992;37(11):1762-1767. https://doi.org/10.1109/9.173146

}

TY - JOUR

T1 - Finite Horizon H∞ Control Problems with Terminal Penalties

AU - Uchida, Kenko

AU - Fujita, Masayuki

PY - 1992

Y1 - 1992

N2 - We generalize the standard H∞ control problem to the finite horizon case with two (possibly singular) terminal penalties at the initial and final times. The major objective of the generalization is to increase flexibility of IF controls. Transients in the finite horizon and the terminal penalties are taken into account within the framework of H∞ control problems. We give a complete solution, a necessary and sufficient condition, and a parameterization to the finite horizon H∞ control problem. The solution is a natural extension of the “Riccati equation” solution. In the special case, when all the terminal penalties vanish, the solution is reduced to the existing one and to the finite horizon standard H∞ control problem. Our approach to the problem is based on completing the square argument of a particular quadratic form, which is at least technically different from the previous ones.

AB - We generalize the standard H∞ control problem to the finite horizon case with two (possibly singular) terminal penalties at the initial and final times. The major objective of the generalization is to increase flexibility of IF controls. Transients in the finite horizon and the terminal penalties are taken into account within the framework of H∞ control problems. We give a complete solution, a necessary and sufficient condition, and a parameterization to the finite horizon H∞ control problem. The solution is a natural extension of the “Riccati equation” solution. In the special case, when all the terminal penalties vanish, the solution is reduced to the existing one and to the finite horizon standard H∞ control problem. Our approach to the problem is based on completing the square argument of a particular quadratic form, which is at least technically different from the previous ones.

UR - http://www.scopus.com/inward/record.url?scp=0000641986&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000641986&partnerID=8YFLogxK

U2 - 10.1109/9.173146

DO - 10.1109/9.173146

M3 - Article

AN - SCOPUS:0000641986

VL - 37

SP - 1762

EP - 1767

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 11

ER -