### Abstract

This paper shows how H^{∞} near-optimal finite-dimensional compensators may be designed for linear time invariant (LTI) infinite-dimensional plants subject to convex constraints. The infinite-dimensional plant is approximated by a finite dimensional approximant. The Youla parameterization is used to parameterize the set of all stabilizing LTI controllers and formulate a weighted mixed-sensitivity H^{∞} optimization that is convex in the Youla Q-Parameter. A finite-dimensional (real-rational) stable basis is used to approximate the Q-parameter. By so doing, we transform the associated infinite-dimensional optimization problem to a finite-dimensional optimization problem involving a search over a finite-dimensional parameter space. In addition to solving weighted mixed-sensitivity H^{∞} control system design problems, subgradient concepts are used to directly accommodate timedomain specifications (e.g. peak value of control action) in the design process. As such, we provide a systematic design methodology for a large class of infinite-dimensional plant control system design problems. In short, the approach taken permits a designer to address control system design problems for which no direct method exists. Convergence results are presented. Illustrative examples for thermal, structural, and aircraft systems are provided.

Original language | English (US) |
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Title of host publication | Proceedings of the IEEE Conference on Decision and Control |

Pages | 1209-1214 |

Number of pages | 6 |

State | Published - 2006 |

Event | 45th IEEE Conference on Decision and Control 2006, CDC - San Diego, CA, United States Duration: Dec 13 2006 → Dec 15 2006 |

### Other

Other | 45th IEEE Conference on Decision and Control 2006, CDC |
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Country | United States |

City | San Diego, CA |

Period | 12/13/06 → 12/15/06 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering
- Safety, Risk, Reliability and Quality
- Chemical Health and Safety

### Cite this

^{∞}mixed-sensitivity optimization for infinite-dimensional plants: Applications to thermal, structural, and aircraft systems. In

*Proceedings of the IEEE Conference on Decision and Control*(pp. 1209-1214). [4178031]

**Constrained H ^{∞} mixed-sensitivity optimization for infinite-dimensional plants : Applications to thermal, structural, and aircraft systems.** / Cifdaloz, Oguzhan; Cartagena, Daniel G.; Rodriguez, Armando.

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

^{∞}mixed-sensitivity optimization for infinite-dimensional plants: Applications to thermal, structural, and aircraft systems. in

*Proceedings of the IEEE Conference on Decision and Control.*, 4178031, pp. 1209-1214, 45th IEEE Conference on Decision and Control 2006, CDC, San Diego, CA, United States, 12/13/06.

^{∞}mixed-sensitivity optimization for infinite-dimensional plants: Applications to thermal, structural, and aircraft systems. In Proceedings of the IEEE Conference on Decision and Control. 2006. p. 1209-1214. 4178031

}

TY - GEN

T1 - Constrained H∞ mixed-sensitivity optimization for infinite-dimensional plants

T2 - Applications to thermal, structural, and aircraft systems

AU - Cifdaloz, Oguzhan

AU - Cartagena, Daniel G.

AU - Rodriguez, Armando

PY - 2006

Y1 - 2006

N2 - This paper shows how H∞ near-optimal finite-dimensional compensators may be designed for linear time invariant (LTI) infinite-dimensional plants subject to convex constraints. The infinite-dimensional plant is approximated by a finite dimensional approximant. The Youla parameterization is used to parameterize the set of all stabilizing LTI controllers and formulate a weighted mixed-sensitivity H∞ optimization that is convex in the Youla Q-Parameter. A finite-dimensional (real-rational) stable basis is used to approximate the Q-parameter. By so doing, we transform the associated infinite-dimensional optimization problem to a finite-dimensional optimization problem involving a search over a finite-dimensional parameter space. In addition to solving weighted mixed-sensitivity H∞ control system design problems, subgradient concepts are used to directly accommodate timedomain specifications (e.g. peak value of control action) in the design process. As such, we provide a systematic design methodology for a large class of infinite-dimensional plant control system design problems. In short, the approach taken permits a designer to address control system design problems for which no direct method exists. Convergence results are presented. Illustrative examples for thermal, structural, and aircraft systems are provided.

AB - This paper shows how H∞ near-optimal finite-dimensional compensators may be designed for linear time invariant (LTI) infinite-dimensional plants subject to convex constraints. The infinite-dimensional plant is approximated by a finite dimensional approximant. The Youla parameterization is used to parameterize the set of all stabilizing LTI controllers and formulate a weighted mixed-sensitivity H∞ optimization that is convex in the Youla Q-Parameter. A finite-dimensional (real-rational) stable basis is used to approximate the Q-parameter. By so doing, we transform the associated infinite-dimensional optimization problem to a finite-dimensional optimization problem involving a search over a finite-dimensional parameter space. In addition to solving weighted mixed-sensitivity H∞ control system design problems, subgradient concepts are used to directly accommodate timedomain specifications (e.g. peak value of control action) in the design process. As such, we provide a systematic design methodology for a large class of infinite-dimensional plant control system design problems. In short, the approach taken permits a designer to address control system design problems for which no direct method exists. Convergence results are presented. Illustrative examples for thermal, structural, and aircraft systems are provided.

UR - http://www.scopus.com/inward/record.url?scp=39649093429&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=39649093429&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:39649093429

SN - 1424401712

SN - 9781424401710

SP - 1209

EP - 1214

BT - Proceedings of the IEEE Conference on Decision and Control

ER -