Hybrid Automata in the Context of Additive Manufacturing

To maintain the forward momentum of additive manufacturing technology, it is necessary to thoroughly evaluate new and potentially useful technological developments in this field. One such development is the intense interest being directed to the field of hybrid automata (HA). Hybrid automata combine both the discrete processing behavior of finite automata as well as the continuous, or flow, behavior of dynamical systems. At this point, some important results on hybrid automata have been obtained, but many open questions remain, including those concerning the decidability of HS operational procedures. (Recall that decidability is directed to a decision problem, that is, a definite true-or-false response given by an effective procedure.) Some important decidability results for HAs have been obtained. For example, in [Henzinger et al.1998] the reachability problem for timed automata (an HA class) has been convincingly shown to be decidable. However, it should also be noted that subtle and difficult issues have been identified, e.g., [Fraenzle 1999], [Asarin, Collins, 2005]. This paper will provide a summary review of the operational features of HAs as they might pertain to additive manufacturing, and then briefly consider the following technical issues: (i) are the classical models of the real numbers best suited to deal with the necessarily approximate measures of physical systems or would non-standard analysis of [Robinson 1996] be a better fit; and (ii) would the introduction of “noisy semantics” and finite arithmetic precision, following [Freidlin, Wentzell 1984], be a better work around?