不确定仿射非线性系统H_∞鲁棒混杂控制

H_∞ Robust Hybrid Control for Uncertain Affine Nonlinear Systems

针对受内部及外部扰动影响的仿射非线性系统,使用切换技术及多Lyapunov函数方法构造出不连续状态反馈控制器,同时设计切换律,使得对于所有允许的不确定性,相应的闭环系统渐近稳定又具有指定的L2增益.主要条件以一组偏微分不等方程给出,其中纯量函数的引入使得不等式组比通常的Hamilton-Jacobi不等式更具有可解性.该方法将一般系统的H∞控制问题转化成了某个切换系统的H∞控制问题.这种混杂状态反馈控制方法对系统参数变化具有很强的鲁棒性.

For an affine nonlinear system affected by internal and external disturbances, the discontinuous state feedback controllers are built by using switching technique and multiple Lyapunov function method with switching laws designed to ensure that for all allowable uncertainties the relevant closed-loop system pcssesses the prescribed L2-gain and is asymptotically stable. The main condition is given in form of a group of partial differential inequalities, among which the inequalities are more solvable than a general Hamilton-Jacobi inequality after introducing the scaler functions. This method fransforms the H∞ control problem of general systems into that of a certain switched system and has strong robustness for the variation of system parameters.