Fuzzy tracking control of fuzzy linear dynamical systems.

Abstract

This paper deals with the fuzzy tracking control problem of a class of uncertain linear dynamical systems. In the uncertain linear dynamical system the uncertainty is considered as fuzzy numbers. This kind of uncertain linear dynamic systems is called fuzzy linear dynamic systems which are expressed in the form of a fuzzy differential equations system. The Mazandarani s approach and the powerful concept of granular differentiability are utilized to deal with the fuzzy differential equations system. Fuzzy tracking control of fuzzy linear dynamic systems looks for a law for the fuzzy control signal by which the output of the system tracks the reference input. In this regard, two fuzzy control laws are proposed under two theorems. First, it is proved that the fuzzy control law is in the form of a fuzzy state feedback with fuzzy gains and an additional term which is a pre-compensator as a fuzzy number. Since in the presence of disturbances this fuzzy control law fails to tackle the problem then other fuzzy control law is proposed under the second theory. Thus, in the second theory, it is proved that the proposed fuzzy controller desirably leads to the output of the fuzzy linear dynamic system tracks the input and the fuzzy disturbance is rejected. In addition, two lemmas regarding the theories are also proved. Moreover, fuzzy tracking control of output of a two tanks in series system and landing jet aircraft are given showing the effectiveness of the proposed approaches.