Practically fast finite-time stability in the mean square of stochastic nonlinear systems with broad learning system

This article examines the fast finite-time stability in the mean square of a class of stochastic nonlinear systems with unmeasurable states. The state of the system under consideration in this article is unmeasurable, in contrast to the conventional finite-time control of stochastic nonlinear systems. First, during the control design process, the corresponding state observer is constructed using the broad learning system technique to solve the state unmeasurable problem. Secondly, in practical applications stochastic disturbance is an unavoidable phenomenon frequently leading to system instability. By combining Itô’s formula and the theory of practically fast finite-time stability in the mean square, adaptive controllers and actual controller are skillfully designed. Meanwhile, the barrier Lyapunov function is adopted to solve the issue that the state of the system is constrained by an asymmetric time-varying function. Finally, the effectiveness of the proposed methodology is illustrated and validated using a cascade chemical reactor system.