A fractal modification of the tropical algebra for noise removal and optimal control

Abstract

This paper proposes a fractal modification of tropical algebra for noise removal and optimal control. Fractal addition, fractal multiplication, and fractal dot product are defined and explained in a fractal space. A fractal tropical polynomials function can model a coastline at any scale, providing a new tool for fractal analysis of any irregular curve. An example is given to solve an optimal control subject to a fractal tropical polynomials function. This paper provides a new window for tropical algebra, combining fractal geometry and algebra.