### Abstract

Design of a robust controller which stabilizes an interval plant from the signal energy point of view via genetic algorithms (GAs) is proposed in this paper. When a controller is placed in series with the interval plant and closed under unity feedback, it is understood that the closed-loop system can also be characterized as an interval family via overbounding. Because stable systems always possess finite impulse response energy, we can obtain the continuous signal energy for each of the four closed-loop vertex systems associated with the four Kharitonov polynomials. With symbolic manipulation of the coefficients of the transfer function of the vertex systems, the parameter identification problem of a robust controller can be transformed into a multi-objective optimization problem. A proposed GA incorporating a fitness assignment mechanism is then used to search for a set of optimal parameters for the controller which stabilizes the interval plant by minimizing the aggregated continuous signal energy of the four vertex systems. The constraints on higher-order plants and controller order commonly encountered by conventional design methods are therefore removed. Several examples are illustrated to demonstrate the effectiveness of the proposed approach.

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

Pages (from-to) | 140-148 |

Number of pages | 9 |

Journal | Control and Intelligent Systems |

Volume | 35 |

Issue number | 2 |

Publication status | Published - 2007 |

Externally published | Yes |

### Fingerprint

### Keywords

- Genetic algorithms
- Interval systems
- Robust control
- Signal energy
- Stabilizing controllers

### ASJC Scopus subject areas

- Hardware and Architecture
- Control and Systems Engineering

### Cite this

*Control and Intelligent Systems*,

*35*(2), 140-148.

**Robust control of interval plants using genetic algorithms.** / Hsu, C. C.; Yu, C. Y.

Research output: Contribution to journal › Article

*Control and Intelligent Systems*, vol. 35, no. 2, pp. 140-148.

}

TY - JOUR

T1 - Robust control of interval plants using genetic algorithms

AU - Hsu, C. C.

AU - Yu, C. Y.

PY - 2007

Y1 - 2007

N2 - Design of a robust controller which stabilizes an interval plant from the signal energy point of view via genetic algorithms (GAs) is proposed in this paper. When a controller is placed in series with the interval plant and closed under unity feedback, it is understood that the closed-loop system can also be characterized as an interval family via overbounding. Because stable systems always possess finite impulse response energy, we can obtain the continuous signal energy for each of the four closed-loop vertex systems associated with the four Kharitonov polynomials. With symbolic manipulation of the coefficients of the transfer function of the vertex systems, the parameter identification problem of a robust controller can be transformed into a multi-objective optimization problem. A proposed GA incorporating a fitness assignment mechanism is then used to search for a set of optimal parameters for the controller which stabilizes the interval plant by minimizing the aggregated continuous signal energy of the four vertex systems. The constraints on higher-order plants and controller order commonly encountered by conventional design methods are therefore removed. Several examples are illustrated to demonstrate the effectiveness of the proposed approach.

AB - Design of a robust controller which stabilizes an interval plant from the signal energy point of view via genetic algorithms (GAs) is proposed in this paper. When a controller is placed in series with the interval plant and closed under unity feedback, it is understood that the closed-loop system can also be characterized as an interval family via overbounding. Because stable systems always possess finite impulse response energy, we can obtain the continuous signal energy for each of the four closed-loop vertex systems associated with the four Kharitonov polynomials. With symbolic manipulation of the coefficients of the transfer function of the vertex systems, the parameter identification problem of a robust controller can be transformed into a multi-objective optimization problem. A proposed GA incorporating a fitness assignment mechanism is then used to search for a set of optimal parameters for the controller which stabilizes the interval plant by minimizing the aggregated continuous signal energy of the four vertex systems. The constraints on higher-order plants and controller order commonly encountered by conventional design methods are therefore removed. Several examples are illustrated to demonstrate the effectiveness of the proposed approach.

KW - Genetic algorithms

KW - Interval systems

KW - Robust control

KW - Signal energy

KW - Stabilizing controllers

UR - http://www.scopus.com/inward/record.url?scp=34250159140&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34250159140&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:34250159140

VL - 35

SP - 140

EP - 148

JO - Mechatronic Systems and Control

JF - Mechatronic Systems and Control

SN - 2561-1771

IS - 2

ER -