### Abstract

For differential geometry based control, the approximation and control scheme studied attempts to resolve the difficulties of accurate modeling and inconvenient calculations by casting the original problem into a simpler form. Given data from the nonlinear system, its state-space is partitioned into cells and an affine-in-state model is determined for each cell by least squares identification. The cell models then constitute an overall piecewise linear system model. Feedback linearization techniques are then performed on the piecewise linear model. The calculations needed to perform the feedback linearization within each cell are shown to be in a simple generic form. The overall controller is formed by joining the individual cell controllers. The results of implementing this control scheme on an example second order nonlinear system show that the resulting controller's performance approaches that of the standard input-state linearization controller.

Original language | English (US) |
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Title of host publication | Proceedings of the American Control Conference |

Publisher | American Automatic Control Council |

Pages | 1344-1348 |

Number of pages | 5 |

Volume | 2 |

State | Published - 1994 |

Externally published | Yes |

Event | Proceedings of the 1994 American Control Conference. Part 1 (of 3) - Baltimore, MD, USA Duration: Jun 29 1994 → Jul 1 1994 |

### Other

Other | Proceedings of the 1994 American Control Conference. Part 1 (of 3) |
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City | Baltimore, MD, USA |

Period | 6/29/94 → 7/1/94 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering

### Cite this

*Proceedings of the American Control Conference*(Vol. 2, pp. 1344-1348). American Automatic Control Council.

**Study of numerical nonlinear control using piecewise linear system approximation.** / Paul, Peter; Phillips, Stephen.

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

*Proceedings of the American Control Conference.*vol. 2, American Automatic Control Council, pp. 1344-1348, Proceedings of the 1994 American Control Conference. Part 1 (of 3), Baltimore, MD, USA, 6/29/94.

}

TY - GEN

T1 - Study of numerical nonlinear control using piecewise linear system approximation

AU - Paul, Peter

AU - Phillips, Stephen

PY - 1994

Y1 - 1994

N2 - For differential geometry based control, the approximation and control scheme studied attempts to resolve the difficulties of accurate modeling and inconvenient calculations by casting the original problem into a simpler form. Given data from the nonlinear system, its state-space is partitioned into cells and an affine-in-state model is determined for each cell by least squares identification. The cell models then constitute an overall piecewise linear system model. Feedback linearization techniques are then performed on the piecewise linear model. The calculations needed to perform the feedback linearization within each cell are shown to be in a simple generic form. The overall controller is formed by joining the individual cell controllers. The results of implementing this control scheme on an example second order nonlinear system show that the resulting controller's performance approaches that of the standard input-state linearization controller.

AB - For differential geometry based control, the approximation and control scheme studied attempts to resolve the difficulties of accurate modeling and inconvenient calculations by casting the original problem into a simpler form. Given data from the nonlinear system, its state-space is partitioned into cells and an affine-in-state model is determined for each cell by least squares identification. The cell models then constitute an overall piecewise linear system model. Feedback linearization techniques are then performed on the piecewise linear model. The calculations needed to perform the feedback linearization within each cell are shown to be in a simple generic form. The overall controller is formed by joining the individual cell controllers. The results of implementing this control scheme on an example second order nonlinear system show that the resulting controller's performance approaches that of the standard input-state linearization controller.

UR - http://www.scopus.com/inward/record.url?scp=0028601168&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028601168&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0028601168

VL - 2

SP - 1344

EP - 1348

BT - Proceedings of the American Control Conference

PB - American Automatic Control Council

ER -