线性离散时不变系统的共轭方向优化迭代学习控制（英文）
发布时间：2019-05-13 17:40
【摘要】：本文针对一类线性离散时不变系统,利用共轭方向优化方法设计了一种迭代学习控制算法.首先,基于采样数据构建超向量,将原二维动态系统转化为迭代域中的一维系统.其次,在这种形式下,利用当前的跟踪误向量减去其在以前搜索方向上的投影,构建新的搜索方向,以补偿当前的控制信号,进而构建下一次迭代的控制信号.再次,结合共轭方向的性质,利用数学归纳法分析了算法的单调收敛性和二次终止性.最后,数值仿真验证了理论分析的正确性和有效性;同时,与已发表的比例型和范数最优迭代学习控制方法进行比较,得出了本算法的优越性.
[Abstract]:In this paper, an iterative learning control algorithm is designed for a class of linear discrete time-invariant systems by using the conjugate direction optimization method. Firstly, the supervector is constructed based on the sampled data, and the original two-dimensional dynamic system is transformed into one-dimensional system in iterative domain. Secondly, in this form, the current tracking error vector is used to subtract its projection in the previous search direction, and a new search direction is constructed to compensate the current control signal, and then the control signal of the next iteration is constructed. Thirdly, combined with the properties of conjugated direction, the monotone convergence and quadratic termination of the algorithm are analyzed by mathematical induction method. Finally, the correctness and effectiveness of the theoretical analysis are verified by numerical simulation, and the advantages of the algorithm are obtained by comparing with the published proportional type and norm optimal iterative learning control methods.
【作者单位】： 西安工程大学理学院;西安交通大学数学与统计学院;
【基金】：The Doctoral Foundation of Xi’an Polytechnic University(BS1617)
【分类号】：O231
[Abstract]:In this paper, an iterative learning control algorithm is designed for a class of linear discrete time-invariant systems by using the conjugate direction optimization method. Firstly, the supervector is constructed based on the sampled data, and the original two-dimensional dynamic system is transformed into one-dimensional system in iterative domain. Secondly, in this form, the current tracking error vector is used to subtract its projection in the previous search direction, and a new search direction is constructed to compensate the current control signal, and then the control signal of the next iteration is constructed. Thirdly, combined with the properties of conjugated direction, the monotone convergence and quadratic termination of the algorithm are analyzed by mathematical induction method. Finally, the correctness and effectiveness of the theoretical analysis are verified by numerical simulation, and the advantages of the algorithm are obtained by comparing with the published proportional type and norm optimal iterative learning control methods.
【作者单位】： 西安工程大学理学院;西安交通大学数学与统计学院;
【基金】：The Doctoral Foundation of Xi’an Polytechnic University(BS1617)
【分类号】：O231
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