非线性迭代学习控制问题的延拓修正牛顿法

A new iterative learning control algorithm of extension-updated Newton method for nonlinear systems

中文关键词  迭代学习控制  延拓法  修正Newton法  全局收敛  非线性系统

英文关键词  iterative learning control  extension method  updated Newton method  global convergence  nonlinear systems

中文摘要

      对于非线性迭代学习控制问题, 提出基于延拓法和修正Newton法的具有全局收敛性的迭代学习控制新方法. 由于一般的Newton型迭代学习控制律都是局部收敛的, 在实际应用中有很大局限性. 为拓宽收敛范围, 该方法将延拓法引入迭代学习控制问题, 提出基于同伦延拓的新的Newton型迭代学习控制律, 使得初始控制可以较为任意的选择. 新的迭代学习控制算法将求解过程分成N个子问题, 每个子问题由换列修正Newton法利用简单的递推公式解出. 本文给出算法收敛的充分条件, 证明了算法的全局收敛性. 该算法对于非线性系统迭代学习控制具有全局收敛和计算简单的优点.

英文摘要

      A new algorithm based on extension method and updated Newton method with global convergence for nonlinear iterative learning control problem is proposed. Since classical Newton-type iterative learning schemes are local convergence, conditions of local convergence can be hardly satisfied in practice. In order to widen the range of convergence, extension method is introduced to iterative learning control problem. A new Newton-type iterative learning control scheme based on homotopy extension is presented, in which the initial control can be chosen arbitrarily. The solving process is subdivided to N subproblem by the new algorithm. The exchange column update Newton method is employed to solve the subproblem by simple recurrent formula. Sufficient conditions for global convergence of this algorithm are given and proved. The implementation of the new algorithm has advantage of guaranteeing global convergence and avoiding complex calculation for nonlinear iterative learning control.