Fuzzy Tracking Control of Fuzzy Linear Dynamical Systems for a fixed reference input under granular derivative

This paper investigates the fuzzy tracking control problem of a class of uncertain linear dynamical systems. The uncertainty of linear dynamical system is considered as fuzzy numbers. This kind of uncertain linear dynamical systems is called fuzzy linear dynamical systems which are expressed in the form of a fuzzy differential equations system. The relative-distance-measure fuzzy interval arithmetic approach and the concept of granular derivatively are utilized to deal with the fuzzy differential equations system. The main aim of designed fuzzy tracking control is to find a fuzzy control law by which the output of the system tracks the reference input. To this end, the fuzzy control law is presented in the form of a theorem. The presented control law is in the form of fuzzy state feedback with fuzzy gains and a fuzzy pre-compensator. Since the system’s states always cannot be measured, a fuzzy observer must be designed to estimate the system’s states. At the end, fuzzy tracking control of output of a two tanks in series system and control of airplane landing are presented to show the effectiveness of the proposed approach.