A max-plus primal space fundamental solution for a class of differential Riccati equations

Recently, a max-plus dual space fundamental solution for a class of difference Riccati equations (DREs) has been developed. This fundamental solution 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 and evolution of the value function of the underlying optimal control problem, a new max-plus primal space fundamental solution for the same class of difference Riccati equations is presented. Connections and commutation results between this new primal space fundamental solution and the recently developed dual space fundamental solution are developed.