Three Basic Theorems in Numerical Analysis in Control Engineering Course and Their Application

• Published in: International journal of control, automation, and systems Vol. 16; no. 5; pp. 2321 - 2333
• Main Authors: Mukaidani, Hiroaki, Shima, Tadashi
• Format: Journal Article
• Language: English
• Published: Bucheon / Seoul Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers 01.10.2018; Springer Nature B.V; 제어·로봇·시스템학회
• Subjects: Control; Control systems; Control systems design; Design engineering; Engineering; Fixed points (mathematics); Iterative methods; Mechatronics; Nonlinear analysis; Nonlinear equations; Numerical analysis; Regular Papers; Robotics; Systems design; Theorems; 제어계측공학; Control engineering course; fixed point theorem; implicit function theorem; Newton-Kantorovich theorem
• ISSN: 1598-6446; 2005-4092
• DOI: 10.1007/s12555-017-0624-y

Control system design packages like MATLAB, SICLAB, OCTAVE, etc. have become essential components of both undergraduate and graduate courses in the field of systems and controls. In particular, the most important subject related to control system design in the undergraduate course is the analysis of a nonlinear equation that is based on iterative methods. In this paper, applications of three basic theorems, –implicit function theorem, Newton-Kantorovich theorem, and fixed point theorem– are proposed to be taught in the numerical analysis in the control engineering course. In order to demonstrate the usefulness of these theorems, several important features are discussed. Furthermore, a practice exercise based on the practical control problem is discussed for proving the useful subject of the numerical analysis in the control engineering course in the graduate level.