Distributed State Estimation for Hybrid and Discrete Event Systems Using l-Complete Approximations

The topic of this paper is distributed state estimation for time-invariant systems with finite input and output spaces. We assume that the system under investigation can be realised by a hybrid I/S/O-machine, where some of the discrete states may also represent failure modes. Our approach is based on previous work, e.g., Moor and Raisch (1999); Moor et al. (2002), where l-complete approximations were proposed as discrete event abstractions for hybrid dynamical systems. In particular, it has been shown that l-complete approximations can be used to provide set-valued estimates for the unknown system state. Estimates are conservative in the sense that the true state can be guaranteed to be contained in the set-valued estimate. In this contribution, we show that for a class of hybrid systems the same estimate can be obtained via a distributed, or decentralised, approach involving several less complex approximations, which are run in parallel. For a larger class of systems, it can be shown that this approach provides an outer approximation of the estimate provided by a monolithic l-complete estimator. The proposed procedure implies significant computational savings during estimator synthesis, with an only modest increase in on-line effort. The latter is a result of “assembling” the global estimate from the available local estimates. The resulting computational trade-off is explicitly discussed.