Efficient State-Estimation of Uncertain Max-Plus Linear Systems with High Observation Noise

This paper presents a new approach to bounded error state-estimation for uncertain max-plus linear systems. This method yields the smallest interval vector including the real state in a guaranteed way. The parameters of the max-plus linear systems are assumed to be bounded, the nondeterministic measurement of the system output is assumed to be given as well as the interval vector including the state at the preceding step. The observation matrix is assumed to be with high noise, i.e., the width of its interval components is large enough. The computation makes intensive use of the residuation theory (Baccelli et al., 1992) over the intervals. This method is worth of interest because it gives a guaranteed over-approximation of the support of the state and could be used to improve the probabilistic approach considered in the literature with an overall complexity of computation lower than existing methods.