### Abstract

This paper studies the set membership state estimation(SMSE) and model validation for continuous-time nonlinear systems with uncertainties. These two problems are formulated as nonlinear optimal tracking problem with reversed time while such optimal problems cannot be solved analytically for nonlinear systems, as for linear systems. This paper proposes a novel approach based on contraction theory to obtain an upper bound of the cost functional of nonlinear tracking problem. Minimizing the upper bound leads to an approximate solution to the nonlinear tracking problem. This approach is applied to the SMSE and model validation problems and it leads to a sufficient condition for the existence of solutions to these two problems. Through minimizing the upper bound, approximate state estimation membership set is obtained. Also, the outline of how to use Sum-of-Square (SOS) programming to compute the solutions is discussed.

Original language | English |
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Title of host publication | Proceedings of 2014 Australian Control Conference, AUCC 2014 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 158-163 |

Number of pages | 6 |

ISBN (Electronic) | 9781922107398 |

DOIs | |

Publication status | Published - Dec 16 2015 |

Event | 4th Australian Control Conference, AUCC 2014 - Canberra, Australia Duration: Nov 17 2014 → Nov 18 2014 |

### Other

Other | 4th Australian Control Conference, AUCC 2014 |
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Country | Australia |

City | Canberra |

Period | 11/17/14 → 11/18/14 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering

### Cite this

*Proceedings of 2014 Australian Control Conference, AUCC 2014*(pp. 158-163). [7358705] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/AUCC.2014.7358705

**Model validation and set membership state estimation for continuous-time nonlinear systems : Contraction metric approach.** / Ouyang, Hua; Manchester, Ian.

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

*Proceedings of 2014 Australian Control Conference, AUCC 2014.*, 7358705, Institute of Electrical and Electronics Engineers Inc., pp. 158-163, 4th Australian Control Conference, AUCC 2014, Canberra, Australia, 11/17/14. https://doi.org/10.1109/AUCC.2014.7358705

}

TY - GEN

T1 - Model validation and set membership state estimation for continuous-time nonlinear systems

T2 - Contraction metric approach

AU - Ouyang, Hua

AU - Manchester, Ian

PY - 2015/12/16

Y1 - 2015/12/16

N2 - This paper studies the set membership state estimation(SMSE) and model validation for continuous-time nonlinear systems with uncertainties. These two problems are formulated as nonlinear optimal tracking problem with reversed time while such optimal problems cannot be solved analytically for nonlinear systems, as for linear systems. This paper proposes a novel approach based on contraction theory to obtain an upper bound of the cost functional of nonlinear tracking problem. Minimizing the upper bound leads to an approximate solution to the nonlinear tracking problem. This approach is applied to the SMSE and model validation problems and it leads to a sufficient condition for the existence of solutions to these two problems. Through minimizing the upper bound, approximate state estimation membership set is obtained. Also, the outline of how to use Sum-of-Square (SOS) programming to compute the solutions is discussed.

AB - This paper studies the set membership state estimation(SMSE) and model validation for continuous-time nonlinear systems with uncertainties. These two problems are formulated as nonlinear optimal tracking problem with reversed time while such optimal problems cannot be solved analytically for nonlinear systems, as for linear systems. This paper proposes a novel approach based on contraction theory to obtain an upper bound of the cost functional of nonlinear tracking problem. Minimizing the upper bound leads to an approximate solution to the nonlinear tracking problem. This approach is applied to the SMSE and model validation problems and it leads to a sufficient condition for the existence of solutions to these two problems. Through minimizing the upper bound, approximate state estimation membership set is obtained. Also, the outline of how to use Sum-of-Square (SOS) programming to compute the solutions is discussed.

UR - http://www.scopus.com/inward/record.url?scp=85002044908&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85002044908&partnerID=8YFLogxK

U2 - 10.1109/AUCC.2014.7358705

DO - 10.1109/AUCC.2014.7358705

M3 - Conference contribution

SP - 158

EP - 163

BT - Proceedings of 2014 Australian Control Conference, AUCC 2014

PB - Institute of Electrical and Electronics Engineers Inc.

ER -