### Abstract

A stochastic fuzzy control is proposed by applying the stochastic control theory, instead of using a traditional fuzzy reasoning. We first solve a control problem of one-step predicted output tracking for linear stochastic systems. Next, we consider a dynamic multiple model adaptive control (MMAC) for the initial data distribution, under the uncertainties of the initial states. We further consider a static MMAC that can be applied for a case of completely unknown plants. It is then shown that a stochastic fuzzy control has some Gaussian potential functions as membership functions and can assign some a priori probabilities to the fuzzy sets or to the control rules, if the probability density function with respect to the output error is replaced by simple characteristic function. It is also cleared that the stochastic fuzzy control becomes a fuzzy control by assuming that all of the a priori probabilities are set to be equal at any control instant.

Original language | English |
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Title of host publication | IEEE International Conference on Fuzzy Systems |

Editors | Anon |

Publisher | IEEE |

Pages | 547-554 |

Number of pages | 8 |

Volume | 2 |

Publication status | Published - 1995 |

Externally published | Yes |

Event | Proceedings of the 1995 IEEE International Conference on Fuzzy Systems. Part 1 (of 5) - Yokohama, Jpn Duration: Mar 20 1995 → Mar 24 1995 |

### Other

Other | Proceedings of the 1995 IEEE International Conference on Fuzzy Systems. Part 1 (of 5) |
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City | Yokohama, Jpn |

Period | 3/20/95 → 3/24/95 |

### Fingerprint

### ASJC Scopus subject areas

- Chemical Health and Safety
- Software
- Safety, Risk, Reliability and Quality

### Cite this

*IEEE International Conference on Fuzzy Systems*(Vol. 2, pp. 547-554). IEEE.

**Stochastic fuzzy control - part I : theoretical derivation.** / Watanabe, Keigo.

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

*IEEE International Conference on Fuzzy Systems.*vol. 2, IEEE, pp. 547-554, Proceedings of the 1995 IEEE International Conference on Fuzzy Systems. Part 1 (of 5), Yokohama, Jpn, 3/20/95.

}

TY - GEN

T1 - Stochastic fuzzy control - part I

T2 - theoretical derivation

AU - Watanabe, Keigo

PY - 1995

Y1 - 1995

N2 - A stochastic fuzzy control is proposed by applying the stochastic control theory, instead of using a traditional fuzzy reasoning. We first solve a control problem of one-step predicted output tracking for linear stochastic systems. Next, we consider a dynamic multiple model adaptive control (MMAC) for the initial data distribution, under the uncertainties of the initial states. We further consider a static MMAC that can be applied for a case of completely unknown plants. It is then shown that a stochastic fuzzy control has some Gaussian potential functions as membership functions and can assign some a priori probabilities to the fuzzy sets or to the control rules, if the probability density function with respect to the output error is replaced by simple characteristic function. It is also cleared that the stochastic fuzzy control becomes a fuzzy control by assuming that all of the a priori probabilities are set to be equal at any control instant.

AB - A stochastic fuzzy control is proposed by applying the stochastic control theory, instead of using a traditional fuzzy reasoning. We first solve a control problem of one-step predicted output tracking for linear stochastic systems. Next, we consider a dynamic multiple model adaptive control (MMAC) for the initial data distribution, under the uncertainties of the initial states. We further consider a static MMAC that can be applied for a case of completely unknown plants. It is then shown that a stochastic fuzzy control has some Gaussian potential functions as membership functions and can assign some a priori probabilities to the fuzzy sets or to the control rules, if the probability density function with respect to the output error is replaced by simple characteristic function. It is also cleared that the stochastic fuzzy control becomes a fuzzy control by assuming that all of the a priori probabilities are set to be equal at any control instant.

UR - http://www.scopus.com/inward/record.url?scp=0029226942&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029226942&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0029226942

VL - 2

SP - 547

EP - 554

BT - IEEE International Conference on Fuzzy Systems

A2 - Anon, null

PB - IEEE

ER -