I. Necoara, E.C. Kerrigan, B. De Schutter, and T.J.J. van den Boom, "Worst-case optimal control of uncertain max-plus-linear systems," Proceedings of the 45th IEEE Conference on Decision and Control, San Diego, California, pp. 6055-6060, Dec. 2006.
In this paper the finite-horizon min-max optimal control problem for uncertain max-plus-linear (MPL) discrete-event systems is considered. We assume that the uncertain parameters lie in a given convex and compact set and it is required that the input and state sequence satisfy a given set of linear inequality constraints. The optimal control policy is computed via dynamic programming using tools from polyhedral algebra and multi-parametric linear programming. Although the controlled system is nonlinear, we provide sufficient conditions, which are usually satisfied in practice, such that the value function is guaranteed to be convex, continuous and piecewise affine, and the optimal control policy is continuous and piecewise affine on a polyhedral domain.