线性离散时不变系统的共轭方向优化迭代学习控制

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.

Conjugate Direction-optimized Iterative Learning Control for Discrete Linear Time-invariant Systems

In this paper, an iterative learning control profile for a class of discrete linear time-invariant systems is designed by employing a conjugate direction optimiza-tion scheme. The control design is formulated in the trial/iteration domain on basis of the lifted system representation, where both input and output sampled during the trials are grouped into super vectors. In this form, the control input signal of the next trial is generated by compensating for the current one with a search-ing direction described as the current tracking error vector minus its projections on historical searching directions. Both monotonic convergence and quadratic ter-mination of the proposed iterative learning control algorithm are analyzed by the technique of the mathematical induction according to the properties of the conju-gate direction. Effectiveness and validity of the control algorithm are illustrated in numerical simulations. Moreover,compared with existing proportional-type and norm-optimal iterative learning control methods, the superiority of the proposed method is also demonstrated.