Adaptive finite‐time stabilization of stochastic nonlinear systems with the powers of positive odd rational numbers

Abstract

In this paper, we give some new results on finite-time stabilization for stochastic nonlinear systems whose powers of integrators are all positive odd rational numbers (ie, numerators and denominators of the powers are all positive odd integers) but not necessary only high order or low order. By adopting new conditions on drift and diffusion terms, Lyapunov function, and controller design method, a state feedback controller is designed to guarantee stochastic nonlinear systems finite-time stable in probability. Moreover, when unknown parameters exist in systems, we give the adaptive finite-time state feedback controller.Numerical examples demonstrate the effectiveness of the proposed results. KEYWORDS adaptive finite-time stabilization, powers of positive odd rational numbers, stochastic nonlinear systems Int

Adaptive fixed‐time tracking control for stochastic pure‐feedback nonlinear systems

“…In the old days, a lot of excellent results have been come out in the field of finite-time adaptive control for stochastic nonlinear systems. [37][38][39][40] Compared with the previously mentioned results which can simply ensure the finite-time stability, we raised a novel scheme to handle the fixed-time stability for stochastic nonlinear system, which indicates that the convergence time of fixed-time control scheme is independent from the initial conditions.…”

“…Nevertheless, to acquire quick convergence and take the stochastic disturbance into consideration, many researches have been obtained. [37][38][39][40] However, there were little research on fixed-time control of stochastic nonlinear systems. As far as we know, the existing fixed-time control design methods are simply valid for deterministic systems, and it will be invalid when applied to the stochastic nonlinear systems.…”

Approximation‐free design for distributed consensus tracking of networked uncertain non‐linear multi‐agent systems with heterogenous high powers

“…In [44], a stabilisation problem for a class of inherently non‐linear systems with output constraints was studied. Some finite‐time stabilisation problems were addressed for high‐order non‐linear systems [45], stochastic high‐order non‐linear systems [46], and output‐constrained high‐order non‐linear systems [47, 48]. A global stabilisation problem for a class of uncertain non‐linear systems with output powers was considered in [49].…”

“…To reduce the complexity of the controller caused by non‐linear bounding functions and function approximators, a low‐complexity tracking control approach was recently presented in [51] and was extended into the decentralised tracking problem of physically interconnected non‐linear power‐chained systems in [52]. However, these works [35–51] only considered the control problem of single or interconnected high‐order non‐linear systems in the power‐chained form. As opposed to these, few results have been developed for the distributed consensus control problem of power‐chained multi‐agent systems under limited communication networks.…”