Finite-time adaptive stabilization of non-strict feedback stochastic nonlinear systems with time-varying coefficients

Abstract

This paper primarily investigates the finite-time stabilization problem for a class of non-strict-feedback stochastic nonlinear systems. In contrast to existing results, this work has two main features: (1) More relaxed assumptions are imposed on the uncertain nonlinearities; (2) unknown parameters appear in both the drift and diffusion terms. Owing to the milder nonlinearity conditions and fewer power constraints, the considered non-strict-feedback system is more general. A state-feedback adaptive finite-time stabilization controller is constructed by employing the backstepping technique and a parameter separation method. The trivial weak solution is strictly proven to be globally stable in probability. The system states will converge to the equilibrium point in finite time. Finally, a simulation result of an actual system is presented to verify the theory proposed in this paper.