输入饱和的非线性系统多模型二阶段自适应控制器设计

Design of multiple-model second level adaptive controller for a class of asymmetric saturation actuators nonlinear system

针对一类输入受限的非线性离散时间系统,设计二阶段自适应控制器.根据先验知识,确定参数空间,在q个未知参数组成的参数空间的边界处建立q+1个自适应模型,将q+1个模型根据自适应系数组合为虚拟模型.基于虚拟模型,通过backstepping方法,设计控制器,采用高斯误差函数近似非对称饱和特性并给出了收敛性证明,得到系统的信号为半全局一致最终有界.最后进行数值仿真,相比于传统自适应控制,该模型能够更快地逼近真实参数,在执行器非对称饱和特性下能够加快系统的响应速度,减小暂态误差,最终的稳态误差收敛于一个较小的紧集,并且对船舶航向控制系统进行了仿真,取得了良好的控制效果.

A second level adaptive controller is designed for a class of nonlinear discrete-time systems subject to input asymmetric saturation. Gauss error function is used to approximate the asymmetric saturation characteristics of actuators.According to the prior knowledge, the parameter space is determined, q+1 adaptive models are built at the boundary of the parameter space composed of q unknown parameters. According to the adaptive coefficient, the q+1 models are combined into a virtual model. Based on the virtual model, the controller is designed by backstepping method, and the stability proof is given. It is proved that under this controller, the signals of the system can be guaranteed to be semi-globally uniform and ultimately bounded. Finally, numerical simulation is carried out. Compared with the traditional adaptive control, the model can approach the real parameters more quickly. Under the asymmetric saturation of actuators, the response speed of the system can be accelerated, the transient error can be reduced, and the final steady-state error converges to a smaller compact set. The ship course control system is simulated and achieved good control effect.