A dynamical interval Newton method

Abstract

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.