### Abstract

In this paper we consider a unified framework for parameter estimation problems which arise in a system identification context. In this framework, the parameters to be estimated appear in a linear fractional transform (LFT) with a known constant matrix M. Through the addition of other nonlinear or time-varying elements in a similar fashion, this framework is capable of treating a wide variety of identification problems, including structured nonlinear systems, linear parameter-varying (LPV) systems, and all of the various parametric linear system model structures. In this paper, we consider both output error and maximum likelihood (ML) cost functions. Using the structure of the problem, we are able to compute the gradient and the Hessian directly, without inefficient finite-difference approximations. Since the LFT structure is general, it allows us to consider issues such as identifiability and persistence of excitation for a large class of model structures, in a single unified framework. Within this framework, there is no distinction between `open-loop' and `closed-loop' identification.

Original language | English (US) |
---|---|

Title of host publication | Proceedings of the American Control Conference |

Publisher | IEEE |

Pages | 2088-2092 |

Number of pages | 5 |

Volume | 3 |

State | Published - 1997 |

Event | Proceedings of the 1997 American Control Conference. Part 3 (of 6) - Albuquerque, NM, USA Duration: Jun 4 1997 → Jun 6 1997 |

### Other

Other | Proceedings of the 1997 American Control Conference. Part 3 (of 6) |
---|---|

City | Albuquerque, NM, USA |

Period | 6/4/97 → 6/6/97 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering

### Cite this

*Proceedings of the American Control Conference*(Vol. 3, pp. 2088-2092). IEEE.

**LFT approach to parameter estimation.** / Wolodkin, Greg; Rangan, Sundeep; Poolla, Kameshwar.

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

*Proceedings of the American Control Conference.*vol. 3, IEEE, pp. 2088-2092, Proceedings of the 1997 American Control Conference. Part 3 (of 6), Albuquerque, NM, USA, 6/4/97.

}

TY - GEN

T1 - LFT approach to parameter estimation

AU - Wolodkin, Greg

AU - Rangan, Sundeep

AU - Poolla, Kameshwar

PY - 1997

Y1 - 1997

N2 - In this paper we consider a unified framework for parameter estimation problems which arise in a system identification context. In this framework, the parameters to be estimated appear in a linear fractional transform (LFT) with a known constant matrix M. Through the addition of other nonlinear or time-varying elements in a similar fashion, this framework is capable of treating a wide variety of identification problems, including structured nonlinear systems, linear parameter-varying (LPV) systems, and all of the various parametric linear system model structures. In this paper, we consider both output error and maximum likelihood (ML) cost functions. Using the structure of the problem, we are able to compute the gradient and the Hessian directly, without inefficient finite-difference approximations. Since the LFT structure is general, it allows us to consider issues such as identifiability and persistence of excitation for a large class of model structures, in a single unified framework. Within this framework, there is no distinction between `open-loop' and `closed-loop' identification.

AB - In this paper we consider a unified framework for parameter estimation problems which arise in a system identification context. In this framework, the parameters to be estimated appear in a linear fractional transform (LFT) with a known constant matrix M. Through the addition of other nonlinear or time-varying elements in a similar fashion, this framework is capable of treating a wide variety of identification problems, including structured nonlinear systems, linear parameter-varying (LPV) systems, and all of the various parametric linear system model structures. In this paper, we consider both output error and maximum likelihood (ML) cost functions. Using the structure of the problem, we are able to compute the gradient and the Hessian directly, without inefficient finite-difference approximations. Since the LFT structure is general, it allows us to consider issues such as identifiability and persistence of excitation for a large class of model structures, in a single unified framework. Within this framework, there is no distinction between `open-loop' and `closed-loop' identification.

UR - http://www.scopus.com/inward/record.url?scp=0030678834&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030678834&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0030678834

VL - 3

SP - 2088

EP - 2092

BT - Proceedings of the American Control Conference

PB - IEEE

ER -