不确定串联非线性系统H∞鲁棒自适应控制

摘要

A robust adaptive controller with L 2-gain is derived for a class of cascaded non-minimum phase nonlinear systems with unknown parameters and disturbances. A recursive Lyapunov-based design approach was developed to construct the controller explicitly so as to avoid solving Hamilton-Jacobi-Isaacs inequality. The state feedback controller guaranteed that the closed system was input-to-state stable and the L2-gain from the disturbance input to the controlled output was not larger than a prescribed value for all admissible parameter uncertainties.In the end,a simulation example was given to demonstrate the controller's feasibility.%针对一类含有未知参数和干扰的非最小相位串联非线性系统,结合H∞控制和自适应控制方法并利用李雅普诺夫函数递推设计方法设计了状态反馈H∞自适应控制器,避免了求解Hamilton-Jacobi-Isaacs不等式设计控制器的困难.该控制器不仅保证闭环系统ISS(input-to-state)稳定,而且使得系统对于所有允许的参数不确定从干扰输入到可控输出的 L 2增益不大于给定的值.最后,给出了一个仿真例子,仿真结果充分表明了所设计的控制器的可行性和有效性.