Design of fuzzy controller using fuzzy Lyapunov synthesis with constrained fuzzy arithmetic

A novel approach to design a fuzzy controller using fuzzy Lyapunov synthesis and constrained fuzzy arithmetic operations in the frame of computing with words is presented. We demonstrate that a set of fuzzy control rules with singleton consequent can be derived systematically, rather than heuristically from perception-based information using the constrained fuzzy arithmetic. The stability of the devised singleton fuzzy controller can be guaranteed by means of fuzzy Lyapunov synthesis that gives a linguistic description on the plant and the control objective. Furthermore, we also show that some deficiencies of the standard fuzzy arithmetic in fuzzy controller design can be overcome by the constrained fuzzy arithmetic which takes all available information into consideration. The performance and applicability of the proposed method are illustrated through the practical implementation of fuzzy control of an autonomous pole-balancing mobile robot.