Joint state and fault estimation for time-varying nonlinear systems with randomly occurring faults and sensor saturations

This paper is concerned with the joint state and fault estimation problem for a class of uncertain time-varying nonlinear stochastic systems with randomly occurring faults and sensor saturations. A random variable obeying the Bernoulli distribution is used to characterize the phenomenon of the randomly occurring faults and the signum function is employed to describe the sensor saturation due to physical limits on the measurement output. The aim of this paper is to design a locally optimal time-varying estimator to simultaneously estimate both the system states and the fault signals such that, at each sampling instant, the covariance of the estimation error has an upper bound that is minimized by properly designing the estimator gain. The explicit form of the estimator gain is characterized in terms of the solutions to two difference equations. It is shown that the developed estimation algorithm is of a recursive form that is suitable for online computations. In addition, the performance analysis of the proposed estimation algorithm is conducted and a sufficient condition is given to verify the exponential boundedness of the estimation error in the mean square sense. Finally, an illustrative example is provided to show the usefulness of the developed estimation scheme.