Adaptive output‐feedback finite‐time stabilisation of stochastic non‐linear systems with application to a two‐stage chemical reactor

In this study, the authors investigate the problem of the stochastically finite‐time stability analysis and control design of an adaptive single‐input and single‐output (SISO) uncertain stochastic non‐linear system via establishing a new stability criterion. Owing to the unknown dynamics and unmeasured system variables, fuzzy logic systems and a fuzzy state observer are constructed and applied to identify the stochastic system, respectively. Combining the finite‐time definition, stochastic differential equation ando ^formula, a novel stochastically finite‐time stability theorem is raised in this study. By utilising the novel criterion and adaptive backstepping intelligent control, a stochastically finite‐time control method is proposed. It is illustrated that the controlled stochastic system is semi‐global finite‐time stable in probability and behaves excellent convergence. The simulation results of a two‐stage continuous stirred tank reactor process reveal the validity and efficiency.