### Abstract

Language | English |
---|---|

Title of host publication | 2018 IEEE Conference on Decision and Control (CDC) |

Place of Publication | PIscataway |

Publisher | Institute of Electrical and Electronics Engineers |

Pages | 1445-1450 |

Number of pages | 6 |

ISBN (Electronic) | 978-1-5386-1395-5 |

ISBN (Print) | 978-1-5386-1396-2 |

DOIs | |

State | Published - 2018 |

Event | 57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States Duration: 17 Dec 2018 → 19 Dec 2018 Conference number: 57 |

### Conference

Conference | 57th IEEE Conference on Decision and Control, CDC 2018 |
---|---|

Abbreviated title | CDC 2018 |

Country | United States |

City | Miami |

Period | 17/12/18 → 19/12/18 |

### Fingerprint

### Cite this

*2018 IEEE Conference on Decision and Control (CDC)*(pp. 1445-1450). PIscataway: Institute of Electrical and Electronics Engineers. DOI: 10.1109/CDC.2018.8619372

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*2018 IEEE Conference on Decision and Control (CDC) .*Institute of Electrical and Electronics Engineers, PIscataway, pp. 1445-1450, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 17/12/18. DOI: 10.1109/CDC.2018.8619372

**On the simulation of polynomial NARMAX models.** / Khandelwal, D.; Schoukens, M.; Toth, R.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - On the simulation of polynomial NARMAX models

AU - Khandelwal,D.

AU - Schoukens,M.

AU - Toth,R.

PY - 2018

Y1 - 2018

N2 - In this paper, we show that the common approach for simulation non-linear stochastic models, commonly used in system identification, via setting the noise contributions to zero results in a biased response. We also demonstrate that to achieve unbiased simulation of finite order NARMAX models, in general, we require infinite order simulation models. The main contributions of the paper are two-fold. Firstly, an alternate representation of polynomial NARMAX models, based on Hermite polynomials, is proposed. The proposed representation provides a convenient way to translate a polynomial NARMAX model to a corresponding simulation model by simply setting certain terms to zero. This translation is exact when the simulation model can be written as an NFIR model. Secondly, a parameterized approximation method is proposed to curtail infinite order simulation models to a finite order. The proposed approximation can be viewed as a trade-off between the conventional approach of setting noise contributions to zero and the approach of incorporating the bias introduced by higher-order moments of the noise distribution. Simulation studies are provided to illustrate the utility of the proposed representation and approximation method.

AB - In this paper, we show that the common approach for simulation non-linear stochastic models, commonly used in system identification, via setting the noise contributions to zero results in a biased response. We also demonstrate that to achieve unbiased simulation of finite order NARMAX models, in general, we require infinite order simulation models. The main contributions of the paper are two-fold. Firstly, an alternate representation of polynomial NARMAX models, based on Hermite polynomials, is proposed. The proposed representation provides a convenient way to translate a polynomial NARMAX model to a corresponding simulation model by simply setting certain terms to zero. This translation is exact when the simulation model can be written as an NFIR model. Secondly, a parameterized approximation method is proposed to curtail infinite order simulation models to a finite order. The proposed approximation can be viewed as a trade-off between the conventional approach of setting noise contributions to zero and the approach of incorporating the bias introduced by higher-order moments of the noise distribution. Simulation studies are provided to illustrate the utility of the proposed representation and approximation method.

U2 - 10.1109/CDC.2018.8619372

DO - 10.1109/CDC.2018.8619372

M3 - Conference contribution

SN - 978-1-5386-1396-2

SP - 1445

EP - 1450

BT - 2018 IEEE Conference on Decision and Control (CDC)

PB - Institute of Electrical and Electronics Engineers

CY - PIscataway

ER -