Discrete state estimators for a class of nondeterministic hybrid systems on a lattice

The problem of estimating the discrete variables in nondeterministic hybrid systems where the continuous variables are available for measurement is considered. Using partial order theory, we construct a discrete state estimator, the LU estimator, which updates the lower (L) and upper (U) bounds of the set of all possible discrete variables values compatible with the output sequence and with the systems´ dynamics. If the system is weakly observable, we show that there always exist a lattice on which to construct the LU estimator. For computational issues, some partial orders are to be preferred to others. We thus show that nondeterminism may be added to a system to obtain a new system that satisfies the requirements for the construction of the LU estimator on a chosen lattice. These ideas are applied to a nondeterministic multi-robot system.