In this paper, a dynamical interval Newton’s method is proposed to solve systems of nonlinear equations. Differently from other interval techniques available in the literature, the proposed method is capable of determining the roots of vector-valued time-varying functions. The design is carried out by firstly proposing an interval Newton’s method capable of determining the roots of a scalar time-varying function and then extending these results to the vector-valued case. If the function to be zeroed is polynomial, then it is shown how to couple the proposed scalar and vector Newton’s methods to determine improved estimates of its roots. Examples of application of the proposed procedure to the inverse kinematics of a robotic manipulator and to the problem of designing an observer for a nonlinear system are reported.

本文提出了一种动态区间牛顿法来求解非线性方程组。与文献中可用的其他间隔技术不同，该方法能够确定矢量值时变函数的根。通过首先提出一种能够确定标量时变函数根的区间牛顿法，然后将这些结果扩展到矢量值的情况来进行设计。如果要归零的函数是多项式，则说明如何将建议的标量和矢量牛顿方法耦合在一起，以确定其根的改进估计。报告了将拟议程序应用于机器人操纵器的逆运动学以及设计非线性系统观察器的问题的示例。