This article concentrates on the output feedback controller design for a class of stochastic nonlinear systems with unknown homogeneous growth rates. First, a full-order observer is proposed coupling with a dynamic gain so as to obtain system state estimates. Then, an adaptive output feedback controller is put forward by the homogeneity theory and adding a power integrator technique. Combined with the stochastic Barbalat’s lemma, the signals of the closed-loop system are demonstrated to be bounded and all the system states are proved to converge to the origin in probability. Besides, the results are also expanded to the controller design of upper-triangular stochastic nonlinear system. Two simulation results indicate usefulness of the designed control algorithm.

本文重点讨论一类具有未知齐次增长率的随机非线性系统的输出反馈控制器设计。首先，提出了与动态增益耦合的全阶观测器，以获得系统状态估计。然后，利用齐次性理论并加入功率积分器技术，提出了一种自适应输出反馈控制器。结合随机 Barbalat 引理，证明闭环系统的信号是有界的，并且证明所有系统状态在概率上收敛到原点。此外，结果还扩展到了上三角随机非线性系统的控制器设计。两个仿真结果表明所设计的控制算法是有用的。