摘要
针对线性时不变控制系统,讨论了D型和P型学习律收敛速度问题.利用时间加权范数和Frobenius范数给出了迭代学习控制系统在D型和P型学习律作用下收敛的充分性条件,进而给出系统迭代次数与约束条件之间的定量关系以及收敛速度与约束条件之间的关系,同时利用Frobenius范数性质,并通过梯度法给出如何求解D型和P型学习律使得系统收敛速度最快的增益矩阵的方法.最后,仿真实例说明了该方法的有效性.
The convergence rate is analyzed for both D-type and P-type learning laws in linear time-invariant control system. A sufficient condition is given by the Frobenius norm and time-weighted norm to guarantee the convergence of D-type and P-type learning lairs. Furthermore, the quantitative relation between iterative number and the relation between convergence rate and constraint condition are given. Simultaneously, the approach to choosing the gain matrix for D-type/P-type learning law so as to get highest convergence rates is given by gradient flow and the property of Frobenius norm. Numerical simulation shows the effectiveness of the proposed method.
出处
《东北大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2006年第8期835-838,共4页
Journal of Northeastern University(Natural Science)
基金
国家自然科学基金资助项目(60574011)
辽宁省普通高校学科带头人基金资助项目(124210)
关键词
迭代学习控制
时间加权范数
学习律
收敛速度
iterative learning control （ILC）
time-weighted norm
learning law
convergence rate
