Robust fault estimation for stochastic nonlinear systems with Brownian perturbations

Motivated by the significance of robust fault estimation of complex systems, the presented paper aims at developing an effective observer for stochastic nonlinear systems subject to partially decoupled unknown inputs from both plant and sensors, so as to estimate the trends of considered faults and states simultaneously, while attenuate the influences from unknown inputs. Firstly, stochastic input-to-state stability of stochastic nonlinear systems is investigated based on Lyapunov theory. The criterion is given in a more simple and straightforward way than previous results regard to the proposed problems. Then an augmented plant is constructed for a quadratic inner-bounded nonlinear system with Brownian motion. An unknown input observer is designed to estimate the trend of augmented state vector, composed of original system states and concerned faults, with a part of unknown inputs decoupled at meantime. The convergence of the estimation error with respect to un-decoupled unknown inputs and Brownian motion is analyzed by the derived stochastic input-to-state stability theorem. Based on linear matrix inequality, the observer gains can be determined to achieve both stability and robustness of the error dynamic. Finally, simulation on a robotic system is shown to prove the effectiveness of the proposed results.