A fault prediction scheme for Takagi-Sugeno fuzzy systems with immeasurable premise variables and disturbance

As explained in the literature, it is very hard to measure premise variables of a Takagi-Sugeno (TS) fuzzy system. Therefore, in this paper, a fault detection and prediction (FDP) scheme is designed for a class of TS fuzzy systems with immeasurable (unknown) premise variables and external disturbances. A fault detection (FD) observer is designed to approximate the system output and the premise variables. Subsequently, a FD residual is generated by comparing the observer output with respect to the system output. The FD residual is evaluated to detect any faults in the system. Further, time-to-failure (TTF) of the TS fuzzy system is obtained by using a mathematical equation. Note the parameter update law and TTF scheme utilize the approximated premise variables since they are not measurable. Stability of the fault detection and TTF prediction results are verified using Lyapunov theory. Finally, a simulation study using a truck-trailer system is presented to verify the theoretical claims.