针对一类分数阶非线性时滞系统,研究其P型迭代学习控制问题。首先,根据分数微积分的基本性质并借助推广的Gronwall不等式,获得系统状态变量的范数不等式估计;然后,通过引入λ-范数,获得在开环和闭环P型迭代学习控制作用下,系统控制输入以及跟踪误差收敛的充分条件。所得结果与已有结果相比,具有更小的保守性。最后,通过数值仿真验证所提方法的有效性。
A P-type iterative learning control (ILC)scheme for a class of fractional order nonlinear time delay systems is presented. First, using properties of the fractional differential calculus and the generalized Gronwall inequality, a norms based inequality for systems state is derived. Second, by introducing the λ-norm, the sufficient conditions for the convergence of the control input and the tracking errors under open loop and closed-loop P-type ILC are obtained, which have less conservative compared with the existing results. Finally, the validity of the proposed method are verified by a numerical example.