title: Transforming the canonical piecewise-linear model into a smooth-piecewise representation.
abstract: A smoothed representation (based on natural exponential and logarithmic functions) for the canonical piecewise-linear model, is presented. The result is a completely differentiable formulation that exhibits interesting properties, like preserving the parameters of the original piecewise-linear model in such a way that they can be directly inherited to the smooth model in order to determine their parameters, the capability of controlling not only the smoothness grade, but also the approximation accuracy at specific breakpoint locations, a lower or equal overshooting for high order derivatives in comparison with other approaches, and the additional advantage of being expressed in a reduced mathematical form with only two types of inverse functions (logarithmic and exponential). By numerical simulation examples, this proposal is verified and well-illustrated.
authors.affiliation: Faculty of Electronic Instrumentation, Universidad Veracruzana, Circuito Gonzalo Aguirre Beltrán S/N, Zona Universitaria, 91000 Xalapa, Veracruz Mexico.
authors.forename: Victor M
authors.initials: VM
authors.lastname: Jimenez-Fernandez
authors.affiliation: Basic Sciences Institute, Universidad Veracruzana, Av. Castelazo Ayala S/N, Col. Industrial Ánimas, 91192 Xalapa, Veracruz Mexico.
authors.forename: Maribel
authors.initials: M
authors.lastname: Jimenez-Fernandez
authors.affiliation: Faculty of Electronic Instrumentation, Universidad Veracruzana, Circuito Gonzalo Aguirre Beltrán S/N, Zona Universitaria, 91000 Xalapa, Veracruz Mexico.
authors.forename: Hector
authors.initials: H
authors.lastname: Vazquez-Leal
authors.affiliation: Faculty of Mathematics, Universidad Veracruzana, Circuito Gonzalo Aguirre Beltrán S/N, Zona Universitaria, 91000 Xalapa, Veracruz Mexico.
authors.forename: Evodio
authors.initials: E
authors.lastname: Muñoz-Aguirre
authors.affiliation: Faculty of Physics, Universidad Veracruzana, Circuito Gonzalo Aguirre Beltrán S/N, Zona Universitaria, 91000 Xalapa, Veracruz Mexico.
authors.forename: Hector H
authors.initials: HH
authors.lastname: Cerecedo-Nuñez
authors.affiliation: Faculty of Electronic Instrumentation, Universidad Veracruzana, Circuito Gonzalo Aguirre Beltrán S/N, Zona Universitaria, 91000 Xalapa, Veracruz Mexico.
authors.forename: Uriel A
authors.initials: UA
authors.lastname: Filobello-Niño
authors.affiliation: Faculty of Electronic Instrumentation, Universidad Veracruzana, Circuito Gonzalo Aguirre Beltrán S/N, Zona Universitaria, 91000 Xalapa, Veracruz Mexico.
authors.forename: Francisco J
authors.initials: FJ
authors.lastname: Castro-Gonzalez
keywords: Canonical; Model; Piecewise-linear; Smooth