State estimation for stochastic delayed neural networks with diffusion terms: A two-step estimation method

This paper proposes an interval estimation scheme for a class of stochastic delayed reaction-diffusion neural networks using a novel two-step estimation method. Different from traditional point estimation methods, the proposed two-step estimation method yields the interval estimation of the expected value of the solution. Based on a robust observer, the pointwise expected value of the solution is first computed. Then, by introducing an auxiliary functional, the bounds of the observation error are derived. Following the results of these two steps, adaptive thresholds for the expected value of the system state are synthesized from the observations and the derived observation error bounds. Moreover, the design of observer gain simultaneously determines both the accuracy of point estimation and the width of the error interval. To make a trade-off between computational cost and estimation accuracy, the peak-to-peak analysis technique is introduced to reduce the computational complexity of high-dimensional systems. Finally, numerical simulation is conducted to demonstrate the effectiveness of the proposed method.