Stochastic Fuzzy Control

(Theoretical Derivation)

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)224-230
Number of pages7
JournalJSME International Journal, Series C: Mechanical Systems, Machine Elements and Manufacturing
Volume40
Issue number2
Publication statusPublished - Jun 1997
Externally publishedYes

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Fuzzy control
Stochastic systems
Membership functions
Fuzzy sets
Control theory
Probability density function

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

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title = "Stochastic Fuzzy Control: (Theoretical Derivation)",
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.",
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author = "Keigo Watanabe",
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journal = "JSME International Journal, Series C: Mechanical Systems, Machine Elements and Manufacturing",
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publisher = "Japan Society of Mechanical Engineers",
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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.

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KW - Hypothesis

KW - Multiple Model

KW - Optimal Control

KW - Predictive Output Feedback Control

KW - Static Model

KW - Stochastic Control

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