### Abstract

In this paper an iterative procedure is developed for synthesizing mixed H
_{2}
/H
_{∞}
robust controllers that satisfy output variance constraints. In this synthesis problem, we seek control-laws for linear systems that minimize an upperbound on a quadratic performance subject to both H
_{∞}
-norm and output variance constraints under the presence of structured uncertainties. The approach taken in this paper is to convert the problem into an equivalent nonlinear programming with both equality and inequality constraints. Kuhn Tucker optimality condition is employed in order to obtain first order necessary condition for a regular point that minimizes an upperbound on quadratic performance for the given H
_{∞}
-norm and variance constraints. Based on this condition, an iterative algorithm for synthesizing the controllers is developed. To demonstrate the effectiveness of the algorithm, an illustrative example is presented. Dual problem that imposes constraints on input variance, is also discussed.

Original language | English |
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Title of host publication | Proceedings of the 1st IEEE Conference on Control Applications, CCA 1992 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 281-286 |

Number of pages | 6 |

ISBN (Electronic) | 0780300475, 9780780300477 |

DOIs | |

Publication status | Published - 1992 Jan 1 |

Event | 1st IEEE Conference on Control Applications, CCA 1992 - Dayton, United States Duration: 1992 Sep 12 → 1992 Sep 16 |

### Publication series

Name | Proceedings of the 1st IEEE Conference on Control Applications, CCA 1992 |
---|

### Conference

Conference | 1st IEEE Conference on Control Applications, CCA 1992 |
---|---|

Country | United States |

City | Dayton |

Period | 92/9/12 → 92/9/16 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Control and Optimization
- Computer Science (miscellaneous)
- Control and Systems Engineering
- Aerospace Engineering
- Industrial and Manufacturing Engineering

### Cite this

_{2}/H

_{∞}robust controllers that satisfy variance constraints In

*Proceedings of the 1st IEEE Conference on Control Applications, CCA 1992*(pp. 281-286). [269862] (Proceedings of the 1st IEEE Conference on Control Applications, CCA 1992). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CCA.1992.269862

**
An algorithm for mixed H
_{2}
/H
_{∞}
robust controllers that satisfy variance constraints
.** / Bambang, Riyanto T.; Shimemura, E.; Uchida, Kenko.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

_{2}/H

_{∞}robust controllers that satisfy variance constraints in

*Proceedings of the 1st IEEE Conference on Control Applications, CCA 1992.*, 269862, Proceedings of the 1st IEEE Conference on Control Applications, CCA 1992, Institute of Electrical and Electronics Engineers Inc., pp. 281-286, 1st IEEE Conference on Control Applications, CCA 1992, Dayton, United States, 92/9/12. https://doi.org/10.1109/CCA.1992.269862

_{2}/H

_{∞}robust controllers that satisfy variance constraints In Proceedings of the 1st IEEE Conference on Control Applications, CCA 1992. Institute of Electrical and Electronics Engineers Inc. 1992. p. 281-286. 269862. (Proceedings of the 1st IEEE Conference on Control Applications, CCA 1992). https://doi.org/10.1109/CCA.1992.269862

}

TY - GEN

T1 - An algorithm for mixed H 2 /H ∞ robust controllers that satisfy variance constraints

AU - Bambang, Riyanto T.

AU - Shimemura, E.

AU - Uchida, Kenko

PY - 1992/1/1

Y1 - 1992/1/1

N2 - In this paper an iterative procedure is developed for synthesizing mixed H 2 /H ∞ robust controllers that satisfy output variance constraints. In this synthesis problem, we seek control-laws for linear systems that minimize an upperbound on a quadratic performance subject to both H ∞ -norm and output variance constraints under the presence of structured uncertainties. The approach taken in this paper is to convert the problem into an equivalent nonlinear programming with both equality and inequality constraints. Kuhn Tucker optimality condition is employed in order to obtain first order necessary condition for a regular point that minimizes an upperbound on quadratic performance for the given H ∞ -norm and variance constraints. Based on this condition, an iterative algorithm for synthesizing the controllers is developed. To demonstrate the effectiveness of the algorithm, an illustrative example is presented. Dual problem that imposes constraints on input variance, is also discussed.

AB - In this paper an iterative procedure is developed for synthesizing mixed H 2 /H ∞ robust controllers that satisfy output variance constraints. In this synthesis problem, we seek control-laws for linear systems that minimize an upperbound on a quadratic performance subject to both H ∞ -norm and output variance constraints under the presence of structured uncertainties. The approach taken in this paper is to convert the problem into an equivalent nonlinear programming with both equality and inequality constraints. Kuhn Tucker optimality condition is employed in order to obtain first order necessary condition for a regular point that minimizes an upperbound on quadratic performance for the given H ∞ -norm and variance constraints. Based on this condition, an iterative algorithm for synthesizing the controllers is developed. To demonstrate the effectiveness of the algorithm, an illustrative example is presented. Dual problem that imposes constraints on input variance, is also discussed.

UR - http://www.scopus.com/inward/record.url?scp=84990736685&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84990736685&partnerID=8YFLogxK

U2 - 10.1109/CCA.1992.269862

DO - 10.1109/CCA.1992.269862

M3 - Conference contribution

AN - SCOPUS:84990736685

T3 - Proceedings of the 1st IEEE Conference on Control Applications, CCA 1992

SP - 281

EP - 286

BT - Proceedings of the 1st IEEE Conference on Control Applications, CCA 1992

PB - Institute of Electrical and Electronics Engineers Inc.

ER -