A new iterative learning control algorithm of extension-updated Newton method for nonlinear systems
非线性迭代学习控制问题的延拓修正牛顿法

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.