### Abstract

This paper proposes an efficient framework for the total least squares (TLS) estimation of differentially flat system states and parameters. Classical ordinary least squares (OLS) estimation assumes: (i) that only the dependent (i.e., output) signals are noisy, and that (ii) the independent (i.e., input) variables are known. In contrast, TLS estimation assumes both the input and output signals to be noisy. Solving TLS problems can be computationally expensive, particularly for nonlinear problems. This challenge arises because the input trajectory must be estimated in a TLS problem, rather than treated as given. This paper addresses this challenge for differentially flat systems by utilizing a pseudospectral expansion to express the input, state, and output trajectories in terms of a flat output trajectory. This transforms the TLS problem into an unconstrained nonlinear programming (NLP) problem with a small number of optimization variables. We demonstrate this framework for an example involving estimating the states and parameters of a second-order nonlinear flat system. Our approach reduces the number of optimization variables from 1503 to 33, while achieving state and parameter estimation errors below 5% and 7%, respectively.

Original language | English (US) |
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Title of host publication | 2016 American Control Conference, ACC 2016 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 5419-5424 |

Number of pages | 6 |

ISBN (Electronic) | 9781467386821 |

DOIs | |

State | Published - Jul 28 2016 |

Event | 2016 American Control Conference, ACC 2016 - Boston, United States Duration: Jul 6 2016 → Jul 8 2016 |

### Publication series

Name | Proceedings of the American Control Conference |
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Volume | 2016-July |

ISSN (Print) | 0743-1619 |

### Other

Other | 2016 American Control Conference, ACC 2016 |
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Country | United States |

City | Boston |

Period | 7/6/16 → 7/8/16 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Electrical and Electronic Engineering

### Cite this

*2016 American Control Conference, ACC 2016*(pp. 5419-5424). [7526519] (Proceedings of the American Control Conference; Vol. 2016-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2016.7526519

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*2016 American Control Conference, ACC 2016.*, 7526519, Proceedings of the American Control Conference, vol. 2016-July, Institute of Electrical and Electronics Engineers Inc., pp. 5419-5424, 2016 American Control Conference, ACC 2016, Boston, United States, 7/6/16. https://doi.org/10.1109/ACC.2016.7526519

**Efficient total least squares state and parameter estimation for differentially flat systems.** / Liu, Ji; Mendoza, Sergio; Li, Guang; Fathy, Hosam Kadry.

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

TY - GEN

T1 - Efficient total least squares state and parameter estimation for differentially flat systems

AU - Liu, Ji

AU - Mendoza, Sergio

AU - Li, Guang

AU - Fathy, Hosam Kadry

PY - 2016/7/28

Y1 - 2016/7/28

N2 - This paper proposes an efficient framework for the total least squares (TLS) estimation of differentially flat system states and parameters. Classical ordinary least squares (OLS) estimation assumes: (i) that only the dependent (i.e., output) signals are noisy, and that (ii) the independent (i.e., input) variables are known. In contrast, TLS estimation assumes both the input and output signals to be noisy. Solving TLS problems can be computationally expensive, particularly for nonlinear problems. This challenge arises because the input trajectory must be estimated in a TLS problem, rather than treated as given. This paper addresses this challenge for differentially flat systems by utilizing a pseudospectral expansion to express the input, state, and output trajectories in terms of a flat output trajectory. This transforms the TLS problem into an unconstrained nonlinear programming (NLP) problem with a small number of optimization variables. We demonstrate this framework for an example involving estimating the states and parameters of a second-order nonlinear flat system. Our approach reduces the number of optimization variables from 1503 to 33, while achieving state and parameter estimation errors below 5% and 7%, respectively.

AB - This paper proposes an efficient framework for the total least squares (TLS) estimation of differentially flat system states and parameters. Classical ordinary least squares (OLS) estimation assumes: (i) that only the dependent (i.e., output) signals are noisy, and that (ii) the independent (i.e., input) variables are known. In contrast, TLS estimation assumes both the input and output signals to be noisy. Solving TLS problems can be computationally expensive, particularly for nonlinear problems. This challenge arises because the input trajectory must be estimated in a TLS problem, rather than treated as given. This paper addresses this challenge for differentially flat systems by utilizing a pseudospectral expansion to express the input, state, and output trajectories in terms of a flat output trajectory. This transforms the TLS problem into an unconstrained nonlinear programming (NLP) problem with a small number of optimization variables. We demonstrate this framework for an example involving estimating the states and parameters of a second-order nonlinear flat system. Our approach reduces the number of optimization variables from 1503 to 33, while achieving state and parameter estimation errors below 5% and 7%, respectively.

UR - http://www.scopus.com/inward/record.url?scp=84992083429&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84992083429&partnerID=8YFLogxK

U2 - 10.1109/ACC.2016.7526519

DO - 10.1109/ACC.2016.7526519

M3 - Conference contribution

T3 - Proceedings of the American Control Conference

SP - 5419

EP - 5424

BT - 2016 American Control Conference, ACC 2016

PB - Institute of Electrical and Electronics Engineers Inc.

ER -