On the set-estimation of uncertain Max-Plus Linear systems

The paper focuses on the set-estimation for uncertain Max-Plus Linear systems, with bounded random parameters. This estimation process involves determining the conditional reach set, which is a compact set of all possible states that can be reached from a previous set through the transition model (dynamics) and can lead to the observed measurements through the observation model. In the context of Bayesian estimation theory, this set represents the support of the posterior probability density function of the system’s state. We compare two approaches, a disjunctive approach, presented in literature, and a concise approach, presented as a contribution of this paper, to exactly compute this set. Even if both approaches are with an exponential theoretical complexity, it is shown that the concise approach is more efficient.