Max-plus 2-norm regression and system identification of max-plus linear dynamical systems with Gaussian noise

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 unregularized problem is not well posed.