一类不确定非线性系统的鲁棒自适应控制

Robust Adaptive Control for a Class of Uncertain Nonlinear Systems

针对一类具有未知控制方向、未知参数以及未建模动态的非线性系统,提出了一种带有死区修正的鲁棒自适应递推控制策略.该策略不需要控制方向符号的先验知识.根据参数的上下界先验信息,分别将光滑投影算法和非连续投影算法与参数自适应律结合起来,既抑制了参数的漂移,又使估计参数达到了最小.算法保证了闭环系统所有信号的有界性,同时使得跟踪误差收敛于零的任意小邻域内.

A robust adaptive hackstepping control scheme with a dead zone modification is proposed for a class of uncertain nonlinear systems with unknown control direction, uncertain parameters and unmodeled dynamics. A priori knowledge of the sign of the control direction is not required. With priori knowledge of the bounds of the parametric uncertainties, the smooth projection method and the discontinuous projection method are incorporated into the adaptive laws to prevent parameter drifts respectively. The number of parameter estimates is minimal for the two cases. It is proved that under the proposed control law, all the closed-loop signals are bounded and the tracking error converges to the any prescribed small interval around zero.