Stable receding horizon control for max-plus-linear systems

Abstract

We develop a stabilizing receding horizon control (RHC) scheme for the class of discrete-event systems called max-pus-linear (MPL) systems. MPL systems can be described by models that are in the max-plus algebra, which has maximization and addition as basic operations. In this paper we extend the concept of positively invariant set from classical system theory to discrete-event MPL systems. We define stability for the class of MPL systems in the sense of Lyapunov. For a particular convex piecewise affine cost function and linear input-state constraints the RHC optimization problem can be recast as a linear program. Using a dual-mode approach we are able to prove exponential stability of the RHC scheme. We derive also a constrained time-optimal controller by solving a sequence of parametric linear programs.