High-order neural network extended state-observer with nuclear application

A high-order neural network extended state observer (HoNN-ESO) is proposed for single-output nonlinear disturbed systems. Under specified condition within a defined set, the HoNN-ESO delivers globally asymptotically bounded observations for state-variables, lumped disturbance and its high-order time-derivatives. By synergistically coupling a multi-layer perception (MLP) with an extended state-observer (ESO), the HoNN-ESO effecitively eliminates the need for high observer gains to compensate for system uncertainties. The inherent unknown nonlinearities in system dynamics are approximated by a custom-designed single-hidden-layer MLP equipped with an online learning law. Increasing the number of hidden-layer neurons can further enhance the overall observation performance. The HoNN-ESO is subsequently applied to the state and disturbance observation of a modular high temperature gas-cooled reactor. Simulation results across five representative scenarios not only validate the theoretical derivations and demonstrate the feasibility of HoNN-ESO in generating smart indicators for anomaly detection, but also verify that satisfactory observation performance can be reliably achieved by appropriately increasing the neuron count.