Finite-horizon min-max control of max-plus-linear systems

In this note, we provide a solution to a class of finite-horizon min-max control problems for uncertain max-plus-linear systems where the uncertain parameters are assumed to lie in a given convex and compact set, and it is required that the closed-loop input and state sequence satisfy a given set of linear inequality constraints for all admissible uncertainty realizations. We provide sufficient conditions such that the value function is guaranteed to be convex and continuous piecewise affine, and such that the optimal control policy is guaranteed to be continuous and piecewise affine on a polyhedral domain.