未知控制方向的迟滞非线性系统预设自适应控制
Prescribed performance adaptive control for nonlinear systems with unknown control direction preceded by hysteresis

针对一类含有迟滞特性的未知控制方向严反馈非线性系统, 设计了基于误差变换的反步自适应控制器. 首 先提出动态迟滞算子来扩展输入空间建立神经网络迟滞模型. 然后利用径向基函数(RBF)神经网络逼近未知函数, 并引入Nussbaum型函数来解决系统未知控制方向问题. 最后采用误差变换将误差限定在预设的范围内, 并利用反 步法设计自适应控制器. 该控制方案不仅能够保证跟踪精度, 还可以提高系统暂态和稳态性能. 仿真结果表明了控 制方案的可行性.
An adaptive backstepping controller is developed for a class of strict-feedback nonlinear systems with hysteresis and unknown control direction. First, a hysteretic operator is employed to construct an augmented input space for transforming the multi-valued mapping of hysteresis into a one-to-one mapping which enables neural networks to model the hysteresis. Then radial basis function (RBF) neural networks are used to approximate the unknown functions, and the unknown control direction is solved by Nussbaum function. Finally, error transformation is used to confine the error to a predefined residual set and an adaptive controller is proposed based on backstepping technique. This control scheme not only guarantees the tracking accuracy, but also improves the transient and steady-state performance. Simulation results show that the control scheme is feasible.