Stochastic Fuzzy Control: (Theoretical Derivation)

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.