Stability analysis of fuzzy control systems using facet functions
The authors point out that the stability and the robustness of control systems are highly desirable features that can only be demonstrated under strict conditions. One of these conditions is the existence of a known plant model. In cases when this model is available, conventional controllers are preferred, to fuzzy ones as they allow the demonstration of the stability of the working conditions. With fuzzy controllers, this appears to be very difficult or even impossible in general cases. Up to now, fuzzy controllers were limited to cases where the plant model was not available, rendering the demonstration of the stability impossible anyway. However, the fuzzy controllers have the advantage of high flexibility and transparence. The article presents a method for the approximation of fuzzy control laws allowing to prove the stability of the system by using facet functions. Essential to this approach is the high flexibility of facet functions, enabling a very good approximation in a fairly large category of practical problems. Further potential for improvement should be sought in the reduction of the processing time. In particular, a joined determination of the Lyapunov function and the approximation of the fuzzy control law seems promising. Another possibility lies in the proper choice of the convex polytopes of the facet functions.
scientific article; zbMATH DE number 891000