Prescribed-time stabilisation of stochastic high-order nonlinear systems with time-varying powers

A control strategy for stochastic nonlinear systems with time-varying high-order dynamics is presented in this paper, which is specifically designed for prescribed-time state-feedback stabilisation. The approach, based on the backstepping design, constructs a time-varying controller, utilising scaled quartic Lyapunov functions and the given scaling function is not used for coordinate transformation. The fundamental characteristic is that the system has a unique and strong solution, almost surely, is implemented for arbitrary initial conditions. The designed scheme ensures mean-square convergence of both state and input within a prescribed time. The validity of the theoretical framework is vividly verified through a numerical example, showcasing the practical application and efficiency of the control method.