Non-singular fixed-time control for uncertain stochastic nonlinear hydraulic systems with randomly varying loads and stochastic sensor disturbances: theory and experiments

Abstract Displacement measurement in hydraulic support systems faces unique challenges from rock burst-induced vibrations that introduce non-smooth stochastic disturbances characterized by Wiener processes. This paper addresses measurement uncertainty in harsh underground environments through a fixed-time control framework. A second-order stochastic nonlinear model is established using Itô calculus to rigorously capture sensor-induced uncertainties. A fixed-time backstepping controller is developed, employing a self-organizing radial basis function neural network to approximate uncertain nonlinearities, with a novel power augmentation term introduced to eliminate singularities while preserving fixed-time convergence. Closed-loop probabilistic stability is proven via stochastic Lyapunov theory. Experimental validation is conducted on a Beckhoff-controlled hydraulic test bench, where Wiener noise is injected into sensor feedback signals to emulate underground stochastic disturbances. Results demonstrate tracking errors within ±2 mm and settling times independent of initial conditions, confirming the effectiveness of the proposed method under realistic measurement uncertainties.