具有反馈信息的PDα-型迭代学习控制律在Lebesgue-p范数意义下的收敛性分析

摘要

This paper proposes a kind of PDα-type fractional-order iterative learning control (ILC) law with feedback information for a class of fractional-order linear time-invariant systems.By taking advantage of the generalize*d Young inequality of convolution integral, the sufficient condition for the monotone convergence of control law is deduced in the sense of Lebesgue-p norm.It is shown that the convergence is determined not only by the learning gains of control law, but also by the attribute of the system itself.And the feedback information may accelerate the convergence speed of PDα-type iterative learning control law when the feedback gains are properly chosen.Simulation results verify the validity of the theory and the effectiveness of the proposed control law.%针对一类分数阶线性时不变系统,提出了具有反馈信息的PDα-型分数阶迭代学习控制律,在Lebesgue-p范数意义下,利用卷积的推广Young不等式,对控制律单调收敛性进行分析,推导出单调收敛的充分条件.分析表明,具有反馈信息的PDα-型迭代学习控制律的收敛性不仅取决于控制律的学习增益,而且依赖于系统自身的属性;同时,若选用适当的反馈增益,可加快迭代学习控制律的收敛速度.仿真实验验证了理论的正确性和控制律的有效性.