An improved fault and state interval estimator for uncertain Takagi-Sugeno fuzzy systems

This paper investigates the simultaneous interval estimation of the fault and state for uncertain Takagi-Sugeno fuzzy systems under the fault. An improved fault and state interval estimator is presented to better estimate the values of fault and state with corresponding tight adaptive intervals. By using the state argument method, the considered system is reformulated in the form of an argument system. Then, based on the $L_1$ optimization method, a novel fault and state interval estimator that can simultaneously and independently minimize the widths of the intervals enclosing each state component is proposed, which has clear geometric meaning and more design freedom degrees. The zonotopic Kalman filter and the observer with K-L structure can be regarded as special forms of the proposed estimator. Finally, we apply the presented approach to a lateral vehicle system to verify the superiority. Compared with the Frobenius norm optimization method and an advanced interval estimation method, the presented approach can improve the performance of the interval estimation and obtain more tight adaptive intervals.