### Abstract

In direct adaptive control, the adaptation mechanism attempts to adjust a parameterized nonlinear controller to approximate an ideal controller. In the indirect case, however, we approximate parts of the plant dynamics that are used by a feedback controller to cancel the system nonlinearities. In both cases, "approximators" such as linear mappings, polynomials, fuzzy systems, or neural networks can be used as either the parameterized nonlinear controller or identifier model. In this paper, we present an algorithm to tune the direction of descent for a gradient-based approximator parameter update law used for a class of nonlinear discrete-time systems in both direct and indirect cases. In our proposed algorithm, the direction of descent is obtained by minimizing the instantaneous control energy. We will show that updating the adaptation gain can be viewed as a special case of updating the direction of descent. Finally, we will illustrate the performance of the proposed algorithm via a simple surge tank example.

Original language | English |
---|---|

Pages (from-to) | 600-605 |

Number of pages | 6 |

Journal | Proceedings of the American Control Conference |

Volume | 1 |

Publication status | Published - 2001 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Control and Systems Engineering

### Cite this

*Proceedings of the American Control Conference*,

*1*, 600-605.

**Stable auto-tuning of the direction of descent for gradient-based nonlinear adaptive control systems.** / Nounou, Hazem; Passino, K. M.

Research output: Contribution to journal › Article

*Proceedings of the American Control Conference*, vol. 1, pp. 600-605.

}

TY - JOUR

T1 - Stable auto-tuning of the direction of descent for gradient-based nonlinear adaptive control systems

AU - Nounou, Hazem

AU - Passino, K. M.

PY - 2001

Y1 - 2001

N2 - In direct adaptive control, the adaptation mechanism attempts to adjust a parameterized nonlinear controller to approximate an ideal controller. In the indirect case, however, we approximate parts of the plant dynamics that are used by a feedback controller to cancel the system nonlinearities. In both cases, "approximators" such as linear mappings, polynomials, fuzzy systems, or neural networks can be used as either the parameterized nonlinear controller or identifier model. In this paper, we present an algorithm to tune the direction of descent for a gradient-based approximator parameter update law used for a class of nonlinear discrete-time systems in both direct and indirect cases. In our proposed algorithm, the direction of descent is obtained by minimizing the instantaneous control energy. We will show that updating the adaptation gain can be viewed as a special case of updating the direction of descent. Finally, we will illustrate the performance of the proposed algorithm via a simple surge tank example.

AB - In direct adaptive control, the adaptation mechanism attempts to adjust a parameterized nonlinear controller to approximate an ideal controller. In the indirect case, however, we approximate parts of the plant dynamics that are used by a feedback controller to cancel the system nonlinearities. In both cases, "approximators" such as linear mappings, polynomials, fuzzy systems, or neural networks can be used as either the parameterized nonlinear controller or identifier model. In this paper, we present an algorithm to tune the direction of descent for a gradient-based approximator parameter update law used for a class of nonlinear discrete-time systems in both direct and indirect cases. In our proposed algorithm, the direction of descent is obtained by minimizing the instantaneous control energy. We will show that updating the adaptation gain can be viewed as a special case of updating the direction of descent. Finally, we will illustrate the performance of the proposed algorithm via a simple surge tank example.

UR - http://www.scopus.com/inward/record.url?scp=0034843097&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034843097&partnerID=8YFLogxK

M3 - Article

VL - 1

SP - 600

EP - 605

JO - Proceedings of the American Control Conference

JF - Proceedings of the American Control Conference

SN - 0743-1619

ER -