### Abstract

In adaptive control algorithms, the adaptation routine (e.g., least squares or gradient) is usually used to adjust the controller parameters to approximate the ideal controller that is assumed to exist. Searching for the ideal parameter vector, a gradient-based hybrid adaptive routine is used here for continuous-time nonlinear systems. The adjustment of the parameter vector is usually based on minimizing the squared error. For direct adaptive control, in this paper an algorithm is presented to adapt the direction of the search vector so that the instantaneous control energy is minimized. Hence, the overall adaptive routine minimizes not only the squares error but also the instantaneous control energy. Stability results of the presented algorithm show that boundedness of the error is dependent on the length of the search vector.

Original language | English |
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Pages (from-to) | 2890-2895 |

Number of pages | 6 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

Volume | 3 |

Publication status | Published - 2003 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Chemical Health and Safety
- Control and Systems Engineering
- Safety, Risk, Reliability and Quality

### Cite this

**Adapting the Direction of the Search Vector for Direct Adaptive Continuous-Time Nonlinear Systems.** / Nounou, Hazem.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Adapting the Direction of the Search Vector for Direct Adaptive Continuous-Time Nonlinear Systems

AU - Nounou, Hazem

PY - 2003

Y1 - 2003

N2 - In adaptive control algorithms, the adaptation routine (e.g., least squares or gradient) is usually used to adjust the controller parameters to approximate the ideal controller that is assumed to exist. Searching for the ideal parameter vector, a gradient-based hybrid adaptive routine is used here for continuous-time nonlinear systems. The adjustment of the parameter vector is usually based on minimizing the squared error. For direct adaptive control, in this paper an algorithm is presented to adapt the direction of the search vector so that the instantaneous control energy is minimized. Hence, the overall adaptive routine minimizes not only the squares error but also the instantaneous control energy. Stability results of the presented algorithm show that boundedness of the error is dependent on the length of the search vector.

AB - In adaptive control algorithms, the adaptation routine (e.g., least squares or gradient) is usually used to adjust the controller parameters to approximate the ideal controller that is assumed to exist. Searching for the ideal parameter vector, a gradient-based hybrid adaptive routine is used here for continuous-time nonlinear systems. The adjustment of the parameter vector is usually based on minimizing the squared error. For direct adaptive control, in this paper an algorithm is presented to adapt the direction of the search vector so that the instantaneous control energy is minimized. Hence, the overall adaptive routine minimizes not only the squares error but also the instantaneous control energy. Stability results of the presented algorithm show that boundedness of the error is dependent on the length of the search vector.

UR - http://www.scopus.com/inward/record.url?scp=1542348659&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1542348659&partnerID=8YFLogxK

M3 - Article

VL - 3

SP - 2890

EP - 2895

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

SN - 0191-2216

ER -