Recursive approach to networked fault estimation with packet dropouts and randomly occurring uncertainties

In this paper, we discuss the fault estimation problem for a class of time-varying networked systems in the simultaneous presence of randomly occurring uncertainties, stochastic nonlinearities and packet dropouts. The phenomena of the randomly occurring uncertainties and packet dropouts are characterized by utilizing mutually independent random variables with known occurrence probabilities. The stochastic nonlinearities are also considered which can cover many known nonlinearities as special cases. The major focus is on the design of the fault estimation algorithm such that, for all randomly occurring uncertainties, stochastic nonlinearities and packet dropouts, an optimized upper bound of the estimation error covariance is derived at each time step and the explicit form of the estimator gain is provided. As a by-product, the unknown system state is estimated simultaneously. It should be noted that a new compensation scheme is introduced to improve the estimation performance by properly using the statistical property of the imperfect measurements. In addition, the monotonicity of the trace of such an optimal upper bound with respect to the missing probability is revealed from theoretical perspective. Finally, the usefulness of the proposed estimation compensation scheme is demonstrated by a simulation example.