### Abstract

The traditional way of thinking in controller design prefers the use of the 'state space representation' introduced by R. Kalman in the early sixties of the past century. This system description is in close relationship with linear or at least partly linear system in which the linear part can be used in forming a quadratic Lyapunov function in the stability proof. In the standard model of such systems it is assumed that the state of the system is not directly observable, only certain linear functions of the state variable are directly measurable. Since such approaches introduce certain feedback gains for the state variable, observers are needed that calculate the estimation of the state variable on the basis of directly measurable quantities. The Luenberger observers solve this task via introducing a differential equation for the estimated state. In order to avoid the mathematical difficulties of Lyapunov's 'direct method' the 'Robust Fixed Point Transformations (RFPT)' were introduced in a novel adaptive technique that instead of the state space representation directly utilized the available approximate model of the system to estimate its 'response function'. In this approach it was assumed that the system's response is directly observable and an iterative sequence was generated by the use of 'Banach's Fixed Point Theorem' that converged to an appropriate deformation of the rough initial model to obtain precise trajectory tracking. In the present paper it is shown that the Luenberger observers and the RFPT-based mathod can be combined in a more conventional approach of the adaptive controllers that are designed on the basis of finding appropriate feedback gains. Illustrative simulation examples are presented to substantiate this statement.

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

Title of host publication | CINTI 2013 - 14th IEEE International Symposium on Computational Intelligence and Informatics, Proceedings |

Pages | 365-369 |

Number of pages | 5 |

DOIs | |

Publication status | Published - 2013 |

Event | 14th IEEE International Symposium on Computational Intelligence and Informatics, CINTI 2013 - Budapest, Hungary Duration: Nov 19 2013 → Nov 21 2013 |

### Other

Other | 14th IEEE International Symposium on Computational Intelligence and Informatics, CINTI 2013 |
---|---|

Country | Hungary |

City | Budapest |

Period | 11/19/13 → 11/21/13 |

### Fingerprint

### ASJC Scopus subject areas

- Artificial Intelligence
- Information Systems

### Cite this

*CINTI 2013 - 14th IEEE International Symposium on Computational Intelligence and Informatics, Proceedings*(pp. 365-369). [6705223] https://doi.org/10.1109/CINTI.2013.6705223

**Application of Luenberger's observer in RFPT-based adaptive control - A case study.** / Kosi, Krisztian; Tar, J.; Haidegger, Tamas.

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

*CINTI 2013 - 14th IEEE International Symposium on Computational Intelligence and Informatics, Proceedings.*, 6705223, pp. 365-369, 14th IEEE International Symposium on Computational Intelligence and Informatics, CINTI 2013, Budapest, Hungary, 11/19/13. https://doi.org/10.1109/CINTI.2013.6705223

}

TY - GEN

T1 - Application of Luenberger's observer in RFPT-based adaptive control - A case study

AU - Kosi, Krisztian

AU - Tar, J.

AU - Haidegger, Tamas

PY - 2013

Y1 - 2013

N2 - The traditional way of thinking in controller design prefers the use of the 'state space representation' introduced by R. Kalman in the early sixties of the past century. This system description is in close relationship with linear or at least partly linear system in which the linear part can be used in forming a quadratic Lyapunov function in the stability proof. In the standard model of such systems it is assumed that the state of the system is not directly observable, only certain linear functions of the state variable are directly measurable. Since such approaches introduce certain feedback gains for the state variable, observers are needed that calculate the estimation of the state variable on the basis of directly measurable quantities. The Luenberger observers solve this task via introducing a differential equation for the estimated state. In order to avoid the mathematical difficulties of Lyapunov's 'direct method' the 'Robust Fixed Point Transformations (RFPT)' were introduced in a novel adaptive technique that instead of the state space representation directly utilized the available approximate model of the system to estimate its 'response function'. In this approach it was assumed that the system's response is directly observable and an iterative sequence was generated by the use of 'Banach's Fixed Point Theorem' that converged to an appropriate deformation of the rough initial model to obtain precise trajectory tracking. In the present paper it is shown that the Luenberger observers and the RFPT-based mathod can be combined in a more conventional approach of the adaptive controllers that are designed on the basis of finding appropriate feedback gains. Illustrative simulation examples are presented to substantiate this statement.

AB - The traditional way of thinking in controller design prefers the use of the 'state space representation' introduced by R. Kalman in the early sixties of the past century. This system description is in close relationship with linear or at least partly linear system in which the linear part can be used in forming a quadratic Lyapunov function in the stability proof. In the standard model of such systems it is assumed that the state of the system is not directly observable, only certain linear functions of the state variable are directly measurable. Since such approaches introduce certain feedback gains for the state variable, observers are needed that calculate the estimation of the state variable on the basis of directly measurable quantities. The Luenberger observers solve this task via introducing a differential equation for the estimated state. In order to avoid the mathematical difficulties of Lyapunov's 'direct method' the 'Robust Fixed Point Transformations (RFPT)' were introduced in a novel adaptive technique that instead of the state space representation directly utilized the available approximate model of the system to estimate its 'response function'. In this approach it was assumed that the system's response is directly observable and an iterative sequence was generated by the use of 'Banach's Fixed Point Theorem' that converged to an appropriate deformation of the rough initial model to obtain precise trajectory tracking. In the present paper it is shown that the Luenberger observers and the RFPT-based mathod can be combined in a more conventional approach of the adaptive controllers that are designed on the basis of finding appropriate feedback gains. Illustrative simulation examples are presented to substantiate this statement.

UR - http://www.scopus.com/inward/record.url?scp=84893732823&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893732823&partnerID=8YFLogxK

U2 - 10.1109/CINTI.2013.6705223

DO - 10.1109/CINTI.2013.6705223

M3 - Conference contribution

AN - SCOPUS:84893732823

SN - 9781479901975

SP - 365

EP - 369

BT - CINTI 2013 - 14th IEEE International Symposium on Computational Intelligence and Informatics, Proceedings

ER -