Event-based state and fault estimation for nonlinear systems with logarithmic quantization and missing measurements

Abstract

This paper mainly focuses on the event-based state and fault estimation problem for a class of nonlinear systems with logarithmic quantization and missing measurements. The sensors are assumed to have different missing probabilities and a constant fault is considered here. Different from a constant threshold in existing event-triggered schemes, the threshold in this paper is varying in the state-independent condition. With resort to the state augmentation approach, a new state vector consisting of the original state vector and the fault is formed, thus the corresponding state and fault estimation problem is transmitted into the recursive filtering problem. By the stochastic analysis approach, an upper bound for the filtering error covariance is obtained, which is expressed by Riccati difference equations. Meanwhile, the filter gain matrix minimizing the trace of the filtering error covariance is also derived. The developed recursive algorithm in the current paper reflects the relationship among the upper bound of the filtering error covariance, the varying threshold, the linearization error, the probabilities of missing measurements and quantization parameters. Finally, two examples are utilized to verify the effectiveness of the proposed estimation algorithm.