分数阶线性时滞系统PD~α型迭代学习控制的鲁棒性

Robustness of PD~α Type Iterative Learning Control for Fractional-order Linear Time-delay Systems

针对一类具有外部有界噪声干扰的分数阶线性时滞系统,利用卷积的推广Young不等式,讨论了PD~α型分数阶迭代学习控制算法(FOILC)在Lebesgue-p(L^p)范数意义下的鲁棒性,获得其鲁棒收敛的条件。理论分析表明,若选取适当的学习增益矩阵,在系统受到外部有界噪声干扰时,随着迭代次数的增加,该算法能够保证系统的跟踪误差一致收敛有界。数值仿真验证了该算法的可行性和理论的正确性。

For a class of fractional-order linear time-delay systems with the bounded external noises,by taking advantage of the generalized Young inequality of convolution integral,the robustness of PD-α type fractional-order iterative learning control（FOILC） was studied in the sense of Lebesgue-p（L-p） norm,and the condition of robustness was obtained.The results manifest that,under some given proper learning gains,through the iterative learning process,the algorithm can guarantee the tracking error are uniform boundedness when the systems are disturbed by the bounded external noises.The succedent simulations support the feasibility of this algorithm and the correctness of the theory.