### Abstract

The Polynomial Nonlinear Auto-Regressive eXogenous input (P-NARX) model, a multivariable polynomial of past input and output values, is a widely used equation error nonlinear system model. The number of model parameters grows rapidly with the polynomial degree, and with the number of past inputs and outputs, but can be reduced significantly by adopting a decoupled structure, consisting of a transformation matrix followed by a bank of single-input single-output polynomials whose outputs are summed to produce the final output. Prediction Error Minimization (PEM) is a classical approach for the identification of both linear and nonlinear systems. Models trained using PEM may not be suitable for system simulation, where the model only has access to the system's inputs. In this paper, an identification method based on Simulation Error Minimization (SEM) for Decoupled P-NARX models is proposed. The proposed algorithm is applied to data from two nonlinear system identification benchmarks and the performance is compared to a previous PEM based algorithm.

Language | English |
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Title of host publication | 2019 American Control Conference, ACC 2019 |

Place of Publication | Piscataway |

Publisher | Institute of Electrical and Electronics Engineers |

Pages | 4362-4367 |

Number of pages | 6 |

ISBN (Electronic) | 978-1-5386-7926-5 |

State | Published - 1 Jul 2019 |

Event | 2019 American Control Conference, ACC 2019 - Philadelphia, United States Duration: 10 Jul 2019 → 12 Jul 2019 http://acc2019.a2c2.org |

### Conference

Conference | 2019 American Control Conference, ACC 2019 |
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Abbreviated title | ACC2019 |

Country | United States |

City | Philadelphia |

Period | 10/07/19 → 12/07/19 |

Internet address |

### Fingerprint

### Cite this

*2019 American Control Conference, ACC 2019*(pp. 4362-4367). [8815172] Piscataway: Institute of Electrical and Electronics Engineers.

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*2019 American Control Conference, ACC 2019.*, 8815172, Institute of Electrical and Electronics Engineers, Piscataway, pp. 4362-4367, 2019 American Control Conference, ACC 2019, Philadelphia, United States, 10/07/19.

**Identification of decoupled polynomial narx model using simulation error minimization.** / Karami, Kiana; Westwick, David; Schoukens, Johan.

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

TY - GEN

T1 - Identification of decoupled polynomial narx model using simulation error minimization

AU - Karami,Kiana

AU - Westwick,David

AU - Schoukens,Johan

PY - 2019/7/1

Y1 - 2019/7/1

N2 - The Polynomial Nonlinear Auto-Regressive eXogenous input (P-NARX) model, a multivariable polynomial of past input and output values, is a widely used equation error nonlinear system model. The number of model parameters grows rapidly with the polynomial degree, and with the number of past inputs and outputs, but can be reduced significantly by adopting a decoupled structure, consisting of a transformation matrix followed by a bank of single-input single-output polynomials whose outputs are summed to produce the final output. Prediction Error Minimization (PEM) is a classical approach for the identification of both linear and nonlinear systems. Models trained using PEM may not be suitable for system simulation, where the model only has access to the system's inputs. In this paper, an identification method based on Simulation Error Minimization (SEM) for Decoupled P-NARX models is proposed. The proposed algorithm is applied to data from two nonlinear system identification benchmarks and the performance is compared to a previous PEM based algorithm.

AB - The Polynomial Nonlinear Auto-Regressive eXogenous input (P-NARX) model, a multivariable polynomial of past input and output values, is a widely used equation error nonlinear system model. The number of model parameters grows rapidly with the polynomial degree, and with the number of past inputs and outputs, but can be reduced significantly by adopting a decoupled structure, consisting of a transformation matrix followed by a bank of single-input single-output polynomials whose outputs are summed to produce the final output. Prediction Error Minimization (PEM) is a classical approach for the identification of both linear and nonlinear systems. Models trained using PEM may not be suitable for system simulation, where the model only has access to the system's inputs. In this paper, an identification method based on Simulation Error Minimization (SEM) for Decoupled P-NARX models is proposed. The proposed algorithm is applied to data from two nonlinear system identification benchmarks and the performance is compared to a previous PEM based algorithm.

UR - http://www.scopus.com/inward/record.url?scp=85072296301&partnerID=8YFLogxK

M3 - Conference contribution

SP - 4362

EP - 4367

BT - 2019 American Control Conference, ACC 2019

PB - Institute of Electrical and Electronics Engineers

CY - Piscataway

ER -