H∞ state estimation for stochastic recurrent neural networks with randomly occurring nonlinearities and variance constraint

Abstract

This paper is coped with the H ∞ state estimation problem under error variance constraint for discrete stochastic recurrent neural networks (RNNs) with parameter uncertainty and randomly occurring nonlinearities. The activation functions satisfy the sector-bounded condition, and the phenomena of randomly occurring nonlinearities are described by random variables obeying Bernoulli distribution. The major purpose is on the development of a time-varying H ∞ state estimation scheme such that some sufficient conditions are derived to ensure both the prescribed H ∞ performance requirement and estimation error variance constraint. Accordingly, the desired estimation algorithm can be realized based on recursive linear matrix inequality approach. Finally, an example is presented to show the effectiveness of the main constrained estimation results.