Constructing Lyapunov functions by verified numerics

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04991
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: The University of Electro-Communications
• Principal Investigator: Yamamoto Nobito 電気通信大学, 大学院情報理工学研究科, 教授 (30210545)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 数値解析 / 精度保証法 / 力学系 / Lyapunov 関数

Outline of Final Research Achievements

Constructing Lyapunov functions by verified numerics has been studied. It is well known that Lyapunov functions are very important tools in order to analyze dynamical systems. Once a Lyapunov function is constructed by verified numerics for a dynamical system, it can be used in mathematical proofs concerning the dynamical system. We have established the methods to construct Lyapunov functions with quadratic forms for continuous and discrete dynamical systems which have hyperbolic equilibria and fixed points, respectively. Our methods also verify areas included by the domain of the Lyapunov functions. Moreover we developed our method and investigated their applications and have obtained several interesting results.

Free Research Field

数値解析、精度保証付き数値計算法