Stochastic fuzzy control - part I: theoretical derivation

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.