一类高次随机非线性系统的自适应动态面控制

针对一类含非线性参数高次随机非线性系统的输出跟踪控制问题，基于自适应增加幂次积分方法，利用参数分离技术和动态面技术，给出了一种自适应光滑状态反馈控制器设计方法。利用Sigmoid函数设计参数自适应律，保证了其导数连续。将低通滤波器引入控制器设计过程，避免了“微分爆炸”现象。通过构造适当形式的控制Lyapunov函数进行稳定性分析，证明了系统输出能被依概率地调节至参考信号的邻域范围。仿真结果验证了所提控制器设计方案的有效性。

Adaptive dynamic surface control for a class of high-order stochastic nonlinear systems

This paper concerned the output tracking problem for a class of high-order stochastic nonlinear systems. Based on the backstepping control by adding a power integrator, an adaptive smooth state-feedback dynamic surface controller was proposed. The derivative of the designed adaption law was continuous by making use of the Sigmoid function. “Explosion of complexity” phenomenon in the adding a power integrator method design was eliminated by introducing a filter at each step of the recursive procedure and employing the dynamic surface control. The stability analysis was carried out by choosing an appropriate conol Lyapunov function. And its results show that the output can be regulated to the small neighborhood of the reference signal in probability. The results of a simulation example demonstrate the effectiveness of the proposed adaptive smooth state-feedback dynamic surface controller.