Max-plus fundamental solution semigroups for a class of difference Riccati equations

Abstract

Recently, a max-plus dual space fundamental solution semigroup for a class of difference Riccati equations (DREs) has been developed. This fundamental solution semigroup is represented in terms of the kernel of a specific max-plus linear operator that plays the role of the dynamic programming evolution operator in a max-plus dual space. In order to fully understand connections between this dual space fundamental solution semigroup and evolution of the value function of the underlying optimal control problem, a new max-plus primal space fundamental solution semigroup for the same class of difference Riccati equations is presented. Connections and commutation results between this new primal sp..