Stochastic fuzzy control (1st report, Theoretical derivation)

A stochastic fuzzy control is proposed by applying the stochastic control theory, instead of using conventional fuzzy reasoning. We first solve a control problem of one-step predicted output tracking for linear stochastic systems. We then derive a dynamic multiple model adaptive control (MMAC) for the initial data distribution, given the uncertainties of the initial states. We further consider a static MMAC that can be applied to the case of completely unknown plants. It is 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 a simple characteristic function. It is also clarified that the stochastic fuzzy control becomes a conventional fuzzy control by assuming that all of the a priori probabilities are equal at any control instant.