15th Triennial World Congress of the International Federation of Automatic Control
  Barcelona, 21–26 July 2002 
FUZZY-ARITHMETIC-BASED LYAPUNOV FUNCTION FOR DESIGN OF FUZZY CONTROLLERS
Changjiu Zhou
School of Electrical and Electronic Engineering
Singapore Polytechnic, 500 Dover Road, Singapore 129784

A novel approach to design fuzzy controllers using fuzzy-arithmetic-based Lyapunov function that gives a linguistic description on the plant and the control objective is presented in this paper. An inverted pendulum system is used as a benchmark dynamic nonlinear plant for evaluating the proposed method. It is shown that a set of stable fuzzy control rules can be derived from perception-based information systematically, rather than heuristically. Based on Lyapunov’s approach, conditions to ensure the stability of a pendulum-cart system are given, and these conditions are then used to verify the perception-based information for balancing a pendulum. Based on these perceptions and standard-fuzzy-arithmetic-based Lyapunov function, a set of traditional fuzzy control rules can be derived. On the other hand, a singleton fuzzy controller can be devised by using constrained-fuzzy-arithmetic-based Lyapunov function. Further more the stability of the fuzzy controllers can be guaranteed by means of fuzzy version of Lyapunov stability analysis. The results obtained are illustrated with a design of stable fuzzy controllers for an autonomous pole balancing mobile robot.
Keywords: Fuzzy control, Lyapunov function, stability, fuzzy sets, robot control
Session slot T-Mo-M04: Fuzzy control theory/Area code 3e : Fuzzy and Neural Systems