### Abstract

Stochastic fuzzy control using stochastic control theory, instead of using conventional fuzzy reasoning, is proposed. We first solve a control problem of one-step predictive output tracking for linear stochastic systems. Next, we consider dynamic multiple model adaptive control (MMAC) for the initial data distribution, under the uncertainties of the initial states. We further consider static MMAC that can be applied for cases of completely unknown plants. It is then shown that a stochastic fuzzy control has some Gaussian potential functions as membership functions and can be used to 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 a simple characteristic function. It is also shown that the stochastic fuzzy control becomes fuzzy control, if all of the a priori probabilities are set to be equal at any control instant.

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

Pages (from-to) | 224-230 |

Number of pages | 7 |

Journal | JSME International Journal, Series C: Mechanical Systems, Machine Elements and Manufacturing |

Volume | 40 |

Issue number | 2 |

Publication status | Published - Jun 1997 |

Externally published | Yes |

### Fingerprint

### Keywords

- Adaptive Control
- Fuzzy Set Theory
- Hypothesis
- Multiple Model
- Optimal Control
- Predictive Output Feedback Control
- Static Model
- Stochastic Control

### ASJC Scopus subject areas

- Industrial and Manufacturing Engineering
- Mechanical Engineering
- Engineering(all)

### Cite this

**Stochastic Fuzzy Control : (Theoretical Derivation).** / Watanabe, Keigo.

Research output: Contribution to journal › Article

*JSME International Journal, Series C: Mechanical Systems, Machine Elements and Manufacturing*, vol. 40, no. 2, pp. 224-230.

}

TY - JOUR

T1 - Stochastic Fuzzy Control

T2 - (Theoretical Derivation)

AU - Watanabe, Keigo

PY - 1997/6

Y1 - 1997/6

N2 - Stochastic fuzzy control using stochastic control theory, instead of using conventional fuzzy reasoning, is proposed. We first solve a control problem of one-step predictive output tracking for linear stochastic systems. Next, we consider dynamic multiple model adaptive control (MMAC) for the initial data distribution, under the uncertainties of the initial states. We further consider static MMAC that can be applied for cases of completely unknown plants. It is then shown that a stochastic fuzzy control has some Gaussian potential functions as membership functions and can be used to 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 a simple characteristic function. It is also shown that the stochastic fuzzy control becomes fuzzy control, if all of the a priori probabilities are set to be equal at any control instant.

AB - Stochastic fuzzy control using stochastic control theory, instead of using conventional fuzzy reasoning, is proposed. We first solve a control problem of one-step predictive output tracking for linear stochastic systems. Next, we consider dynamic multiple model adaptive control (MMAC) for the initial data distribution, under the uncertainties of the initial states. We further consider static MMAC that can be applied for cases of completely unknown plants. It is then shown that a stochastic fuzzy control has some Gaussian potential functions as membership functions and can be used to 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 a simple characteristic function. It is also shown that the stochastic fuzzy control becomes fuzzy control, if all of the a priori probabilities are set to be equal at any control instant.

KW - Adaptive Control

KW - Fuzzy Set Theory

KW - Hypothesis

KW - Multiple Model

KW - Optimal Control

KW - Predictive Output Feedback Control

KW - Static Model

KW - Stochastic Control

UR - http://www.scopus.com/inward/record.url?scp=2542482950&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2542482950&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:2542482950

VL - 40

SP - 224

EP - 230

JO - JSME International Journal, Series C: Mechanical Systems, Machine Elements and Manufacturing

JF - JSME International Journal, Series C: Mechanical Systems, Machine Elements and Manufacturing

SN - 1344-7653

IS - 2

ER -