Smooth Compositions Enhance Safety of the Fuzzy Systems

Fuzzy models provide an empirical structure for controller design upon the experience of the operator, where the system output is delivered from a block box. Hence, there is a lack of effective way for assuring the safety specifications during the system transitions. This is to say, there are safety-oriented restrictions where the system stated are prohibited to enter under the fuzzy based controller paradigm, however, the system transitions are not visible to the designer. Therefore, the safety margin of the fuzzy controlled systems is limited, since, when data arriving to the closed loop system have considerable level of noises and uncertainties, then, the standard fuzzy models will have difficulties to face the unpredicted conditions of closed loop system. Hence, the current paper proposes that the employment of the smooth fuzzy models will assist highly in avoiding the states enter to the critical areas. In this regards, we have defined reachability diameter of the fuzzy model and proved that the fuzzy models with the so-called smooth fuzzy compositions can potentially have more safe functioning in the closed loop systems rather than standard fuzzy models due to the of the tighter reachability diameter and their Lipschitz continuity characters. It will result to their higher robust performance and this claim has been supported by different simulations of the examples.