Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
ISSN-L : 2185-4106
Special Issue on Recent Progress in Nonlinear Theory and Its Applications
Piecewise linear switched dynamical systems: A review
Toshimichi Saito
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2020 Volume 11 Issue 4 Pages 373-390

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Abstract

This review paper introduces piecewise linear switched dynamical systems in three topics. In the first topic of autonomous chaotic circuits, we introduce the manifold piecewise linear system and chaotic spiking oscillator. Using piecewise exact solutions and mapping procedure, we obtain rigorous proof of chaos generation. In the second topic of recurrent neural networks, we introduce the hysteresis neural network and its application to associative memories. Performing theoretical analysis based on the piecewise exact solutions, we obtain parameter conditions for guaranteed storage of any desired memories. In the third topic of multiobjective optimization problems, we introduce a two-objective problem in a piecewise linear model of switching power converter with photovoltaic input. Applying a simple multiobjective evolutionary algorithm, we clarify existence of a trade-off between the maximum input power and circuit stability.

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© 2020 The Institute of Electronics, Information and Communication Engineers
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