A dynamical interval Newton method

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...

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Bibliographic Details
Published in:European journal of control Vol. 59; pp. 290 - 300
Main Authors: Menini, Laura, Possieri, Corrado, Tornambè, Antonio
Format: Journal Article
Language:English
Published: Philadelphia Elsevier Ltd 01.05.2021
Elsevier Limited
Subjects:
Algebra
Geometry
Interval estimation
Inverse kinematics
Kinematics
Mathematical analysis
Methods
Newton methods
Nonlinear equations
Nonlinear systems
Observer design
Polynomial methods
Polynomials
Robot arms
Robotic manipulators
Root finding algorithm
Polynomial methods
Interval estimation
Robotic manipulators
Root finding algorithm
Observer design
ISSN:0947-3580, 1435-5671
Online Access:Get full text
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Summary: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.
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ISSN:0947-3580
1435-5671
DOI:10.1016/j.ejcon.2020.10.004