This paper studies the adaptive state feedback stabilization problem of stochastic nonlinear systems with many uncertainties, such as parametric uncertainties, time-varying delay, unknown powers and stochastic inverse dynamics. By virtue of the adding-a-power-integrator technique, an adaptive control scheme together with a novel state feedback control law is proposed to deal with these unknowns. Compared with the existing literature, both of adaptive dynamics, higher and lower powers are introduced into the construction of our controller. Based on some ideas of Lyapunov function, we analyze the global stabilization of the whole system. Finally, a simulation example is given to show the effectiveness of our theoretical results.

The problem of designing C ¹ or C ^∞ controllers for a class of stochastic nonlinear systems (SNSs) in lower-triangular form is studied in this note. By using the well-known backstepping method, the concept of homogeneity with monotone degrees (HWMD) and the sign function approach, we construct a C ¹ state feedback controller recursively. Meanwhile, by employing a polynomial Lyapunov function with sign functions, we prove that the solution to SNSs is globally asymptotically stable in probability. Furthermore, based on the concept of HWMD, it shows that C ¹ controllers for a class of three-dimensional SNSs can be modified to C∞ controllers under certain conditions. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed controllers.

In this study, the problem of adaptive state feedback stabilisation of switched stochastic non‐linear systems is addressed. To overcome the uncertainty of arbitrary switchings, a novel common Lyapunov function is constructed in the authors' control scheme. By integrating adaptive control technique and homogeneity with monotone degrees into backstepping framework, a common state feedback control law independent of switching signal is designed recursively under weaker non‐linear growth conditions. A distinct feature of non‐linear conditions is that the parameters ( ) can be chosen as different values rather than a unified value in the existing literature. Finally, a simulation example is presented to show the effectiveness of their control scheme.