Robust invariance in uncertain discrete event systems with applications to transportation networks

This paper studies a class of uncertain discrete event systems over the max-plus algebra, where system matrices are unknown but are convex combinations of known matrices. These systems model a wide range of applications, for example, transportation systems with varying vehicle travel time and queueing networks with uncertain arrival and queuing time. This paper presents computational methods for different robust invariant sets of such systems. A recursive algorithm is given to compute the supremal robust invariant sub-semimodule in a given sub-semimodule. The algorithm converges to a fixed point in a finite number of iterations under proper assumptions on the state semimodule. This paper also presents computational methods for positively robust invariant polyhedral sets. A search algorithm is presented for the positively robust invariant polyhedral sets. The main results are applied to the time table design of a public transportation network.