Max-plus Linear Inverse Problems: 2-norm regression and system identification of max-plus linear dynamical systems with Gaussian noise
It provides a novel framework for regression and system identification in max-plus algebra, addressing a gap for problems with Gaussian noise.
This paper develops theory and algorithms for 2-norm regression over the max-plus semiring, and applies it to system identification of max-plus linear dynamical systems with Gaussian noise, including regularized inverse problems for ill-posed cases.
In this paper we present new theory and algorithms for 2-norm regression over the max-plus semiring. As an application we also show how max-plus 2-norm regression can be used in system identification of max-plus linear dynamical systems with Gaussian noise. We also introduce and provide methods for solving a max-plus linear inverse problem with regularization, which can be used when the the original problem is not well posed.