Modeling nonlinear systems using multiple piecewise linear equations

This paper describes a technique for modeling nonlinear systems using multiple piecewise linear equations. The technique provides a means for linearizing the nonlinear system in such a way as to not limit the large signal behavior of the target system. The nonlinearity in the target system must be able to be represented as a piecewise linear function. A simple third order nonlinear system is used to demonstrate the technique. The behavior of the modeled system is compared to the behavior of the nonlinear system.

Download Full-text

Spectral Characteristics of Nonlinear Systems Approximated by Piecewise Linear Function

Seventh International Conference on Networking (icn 2008) ◽

10.1109/icn.2008.63 ◽

2008 ◽

Author(s):

Jiri Schimmel ◽

Ivan Koula ◽

Jiri Misurec ◽

Zdenek Smekal

Keyword(s):

Nonlinear Systems ◽

Linear Function ◽

Piecewise Linear ◽

Spectral Characteristics ◽

Piecewise Linear Function

Download Full-text

MINLP formulations for continuous piecewise linear function fitting

Computational Optimization and Applications ◽

10.1007/s10589-021-00268-5 ◽

2021 ◽

Author(s):

Noam Goldberg ◽

Steffen Rebennack ◽

Youngdae Kim ◽

Vitaliy Krasko ◽

Sven Leyffer

Keyword(s):

Linear Function ◽

Piecewise Linear ◽

Piecewise Linear Function ◽

Mixed Integer ◽

Function Fitting ◽

Computational Performance ◽

Integer Nonlinear Programming ◽

Minlp Model ◽

Necessary Constraints ◽

Continuous Piecewise Linear Function

AbstractWe consider a nonconvex mixed-integer nonlinear programming (MINLP) model proposed by Goldberg et al. (Comput Optim Appl 58:523–541, 2014. 10.1007/s10589-014-9647-y) for piecewise linear function fitting. We show that this MINLP model is incomplete and can result in a piecewise linear curve that is not the graph of a function, because it misses a set of necessary constraints. We provide two counterexamples to illustrate this effect, and propose three alternative models that correct this behavior. We investigate the theoretical relationship between these models and evaluate their computational performance.

Download Full-text

DESIGN OF TIME DELAYED CHAOTIC CIRCUIT WITH THRESHOLD CONTROLLER

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127411028751 ◽

2011 ◽

Vol 21 (03) ◽

pp. 725-735 ◽

Cited By ~ 16

Author(s):

K. SRINIVASAN ◽

I. RAJA MOHAMED ◽

K. MURALI ◽

M. LAKSHMANAN ◽

SUDESHNA SINHA

Keyword(s):

Numerical Simulations ◽

Linear Function ◽

Piecewise Linear ◽

Piecewise Linear Function ◽

Operational Amplifiers ◽

Phase Portraits ◽

Chaotic Attractors ◽

Chaotic Oscillator ◽

Threshold Values ◽

Chaotic Circuit

A novel time delayed chaotic oscillator exhibiting mono- and double scroll complex chaotic attractors is designed. This circuit consists of only a few operational amplifiers and diodes and employs a threshold controller for flexibility. It efficiently implements a piecewise linear function. The control of piecewise linear function facilitates controlling the shape of the attractors. This is demonstrated by constructing the phase portraits of the attractors through numerical simulations and hardware experiments. Based on these studies, we find that this circuit can produce multi-scroll chaotic attractors by just introducing more number of threshold values.

Download Full-text