### Abstract

The problem of mixed H_{2}/H_{∞} control with pole placement is considered for linear time-invariant systems. This is the problem of determining a controller for linear time-invariant systems which minimizes the H_{2}-norm of a certain closed-loop transfer function subject to an H_{∞}-norm constraint on another closed-loop transfer function and an additional constraint on the location of the closed-loop poles in the complex plane. An optimization problem is posed for the pole-constrained H_{2}/H_{∞} problem in such a way that the objective function is expressed as a weighted sum of the actual H_{2} cost and its upper bound. A necessary condition for the optimization problem is derived via the Lagrange multiplier technique. The condition involves a set of highly coupled equations. By sacrificing the H_{2} performance, an alternative optimization problem is posed in order to simplify the necessary condition. An iterative algorithm for solving the coupled equations arising in the necessary conditions is proposed and numerical examples are presented.

Original language | English |
---|---|

Pages (from-to) | 151-173 |

Number of pages | 23 |

Journal | Optimal Control Applications and Methods |

Volume | 15 |

Issue number | 3 |

Publication status | Published - 1994 Jul |

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### ASJC Scopus subject areas

- Management Science and Operations Research
- Control and Systems Engineering
- Applied Mathematics
- Control and Optimization

### Cite this

_{2}/H

_{∞}control with pole placement in a class of regions.

*Optimal Control Applications and Methods*,

*15*(3), 151-173.

**Mixed H _{2}/H_{∞} control with pole placement in a class of regions.** / Bambang, Riyanto T.; Shimemura, Etsujiro; Uchida, Kenko.

Research output: Contribution to journal › Article

_{2}/H

_{∞}control with pole placement in a class of regions',

*Optimal Control Applications and Methods*, vol. 15, no. 3, pp. 151-173.

_{2}/H

_{∞}control with pole placement in a class of regions. Optimal Control Applications and Methods. 1994 Jul;15(3):151-173.

}

TY - JOUR

T1 - Mixed H2/H∞ control with pole placement in a class of regions

AU - Bambang, Riyanto T.

AU - Shimemura, Etsujiro

AU - Uchida, Kenko

PY - 1994/7

Y1 - 1994/7

N2 - The problem of mixed H2/H∞ control with pole placement is considered for linear time-invariant systems. This is the problem of determining a controller for linear time-invariant systems which minimizes the H2-norm of a certain closed-loop transfer function subject to an H∞-norm constraint on another closed-loop transfer function and an additional constraint on the location of the closed-loop poles in the complex plane. An optimization problem is posed for the pole-constrained H2/H∞ problem in such a way that the objective function is expressed as a weighted sum of the actual H2 cost and its upper bound. A necessary condition for the optimization problem is derived via the Lagrange multiplier technique. The condition involves a set of highly coupled equations. By sacrificing the H2 performance, an alternative optimization problem is posed in order to simplify the necessary condition. An iterative algorithm for solving the coupled equations arising in the necessary conditions is proposed and numerical examples are presented.

AB - The problem of mixed H2/H∞ control with pole placement is considered for linear time-invariant systems. This is the problem of determining a controller for linear time-invariant systems which minimizes the H2-norm of a certain closed-loop transfer function subject to an H∞-norm constraint on another closed-loop transfer function and an additional constraint on the location of the closed-loop poles in the complex plane. An optimization problem is posed for the pole-constrained H2/H∞ problem in such a way that the objective function is expressed as a weighted sum of the actual H2 cost and its upper bound. A necessary condition for the optimization problem is derived via the Lagrange multiplier technique. The condition involves a set of highly coupled equations. By sacrificing the H2 performance, an alternative optimization problem is posed in order to simplify the necessary condition. An iterative algorithm for solving the coupled equations arising in the necessary conditions is proposed and numerical examples are presented.

UR - http://www.scopus.com/inward/record.url?scp=0028465971&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028465971&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0028465971

VL - 15

SP - 151

EP - 173

JO - Optimal Control Applications and Methods

JF - Optimal Control Applications and Methods

SN - 0143-2087

IS - 3

ER -