### Abstract

This paper shows how ℋ^{∞} near-optimal finite-dimensional compensators may be designed for stable 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 from 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 time-domain 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. An illustrative example for a thermal diffusion process is also provided.

Original language | English (US) |
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Title of host publication | Proceedings of the American Control Conference |

Pages | 1009-1014 |

Number of pages | 6 |

Volume | 2006 |

State | Published - 2006 |

Event | 2006 American Control Conference - Minneapolis, MN, United States Duration: Jun 14 2006 → Jun 16 2006 |

### Other

Other | 2006 American Control Conference |
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Country | United States |

City | Minneapolis, MN |

Period | 6/14/06 → 6/16/06 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering

### Cite this

^{∞}mixed-sensitivity optimization for stable infinite-dimensional plants: Application to thermal diffusion process. In

*Proceedings of the American Control Conference*(Vol. 2006, pp. 1009-1014). [1655491]

**Constrained ℋ ^{∞} mixed-sensitivity optimization for stable infinite-dimensional plants : Application to thermal diffusion process.** / Cifdaloz, Oguzhan; Rodriguez, Armando.

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

^{∞}mixed-sensitivity optimization for stable infinite-dimensional plants: Application to thermal diffusion process. in

*Proceedings of the American Control Conference.*vol. 2006, 1655491, pp. 1009-1014, 2006 American Control Conference, Minneapolis, MN, United States, 6/14/06.

^{∞}mixed-sensitivity optimization for stable infinite-dimensional plants: Application to thermal diffusion process. In Proceedings of the American Control Conference. Vol. 2006. 2006. p. 1009-1014. 1655491

}

TY - GEN

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

T2 - Application to thermal diffusion process

AU - Cifdaloz, Oguzhan

AU - Rodriguez, Armando

PY - 2006

Y1 - 2006

N2 - This paper shows how ℋ∞ near-optimal finite-dimensional compensators may be designed for stable 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 from 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 time-domain 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. An illustrative example for a thermal diffusion process is also provided.

AB - This paper shows how ℋ∞ near-optimal finite-dimensional compensators may be designed for stable 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 from 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 time-domain 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. An illustrative example for a thermal diffusion process is also provided.

UR - http://www.scopus.com/inward/record.url?scp=34047213310&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34047213310&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:34047213310

SN - 1424402107

SN - 9781424402106

VL - 2006

SP - 1009

EP - 1014

BT - Proceedings of the American Control Conference

ER -