Distributed resilient estimation over sensor networks for nonlinear time-delayed systems with stochastic perturbations

This paper is concerned with the distributed resilient estimation problem for a class of nonlinear time-delayed systems subject to stochastic perturbations. The plant and the measurements are disturbed by two Gaussian white stochastic processes with known statistical information, respectively. In addition, a resilient estimator is designed for each node by means of the parameter uncertainties and Bernoulli-distributed random variables. Then, a novel exponential-bounded performance index is put forward to measure the disturbance rejection level of the distributed estimators against the external disturbances and the impact of the initial values. A new vector dissipation definition including multiple vectors of energy storage functions is established to deal with the time-delay estimation error dynamics. Within the framework of local performance analysis inspired by this new definition of vector dissipation, sufficient conditions in terms of recursive linear matrix inequalities are constructed for each node to guarantee the desirable performance index. Next, a local optimization problem subject to a set of recursive linear matrix inequalities is presented for each node to minimize the upper bound in the performance index, where the calculations can be conducted on every node in a distributed manner and the estimator gains are also calculated. Finally, an illustrative simulation example is provided to verify the applicability of the proposed estimators.