A fuzzy arithmetical approach to robust control

A fuzzy arithmetical approach to effectively control systems with uncertain model parameters is presented. The approach is mainly based on a combination of classical controller design and fuzzy arithmetic. The uncertainties in the system model are expressed by fuzzy-valued model parameters with their membership functions derived from experimental data or expert knowledge. Subsequently, classical controller design is used to determine the parameters of the controller, making use of fuzzy arithmetic to evaluate the fuzzy-valued controller equations. To avoid the overestimation effect as the major problem of standard fuzzy arithmetic, a special implementation of fuzzy arithmetic, namely the transformation method, is introduced in this paper. On this basis, a robust, fuzzy-parameterized linear-quadratic regulator is developed and finally applied to stabilize an inverted double pendulum with uncertain model parameters in its upright position