On The Double Newton Method for Solving Fuzzy Quadratic Linear Control Form
Zani Anjani Rafsanjani Hsm (a,b)*, Hilal Akmal Almubarok Perdana Adiputra (b), Sugiyarto Surono (b)

(a) Department of Mathematics, Faculty of Science and Mathematics, Diponegoro University, Semarang, Indonesia
*zani.anjani4[at]gmail.com, zani[at]lecturer.undip.ac.id

(b) Department of Mathematics, Faculty of Science and Applied Technology, Ahmad Dahlan University, Yogyakarta, Indonesia

Abstract

Quadratic linear control is a mathematical system of equations modeled from various life phenomena. However, there are numerous problems associated with the process of optimizing linear quadratic control in real life, such as the inability to express the variables numerically. We provide a different way to solve the system using fuzzy logic transformation to determine the optimal solution of quadratic linear controls. The dynamic control system consist of the linear performance index and a quadratic constraint. This system transformed with Triangular Fuzzy Number, which formed a multi-objective optimization model. Furthermore, the optimal control function can be determined with some calculation. Hance, to find the optimal solution of the system, the Lyapunov functions will be solved using some numerical methods. In this case, we modify the original Newton Methods and Double Newton Method for the Quadratic Linear Control Fuzzy form. Some numerical examples are given to show the effectiveness of the algorithms. The results shows that The Newton Method and The Double Newton methods gives a good performance to find the optimal control

Keywords: fuzzy quadratic control- newton method- double newton method

Topic: MATHEMATICS AND STATISTICS