Observability of Discrete Event Dynamic Systems

A finite state automaton is adopted as a model for Discrete Event Dynamic Systems (DEDS). Observations are assumed to be a subset of the event alphabet. Observability is defined as having perfect knowledge of the current state at points in time seperated by bounded numbers of transitions. A polynomial test for observability is given. It is shown that an observer may be constructed and implemented in polynomial time and space. A bound on the cardinality of the observer state space is also presented. A notion of resiliency is defined for observers, and a test for resilient observability and a procedure for the construction of a resilient observer are presented. 1 Research supported by the Air Force Office of Scientific Research under Grant AFOSR-88-0032 and by the Army Research Office under Grant DAAL03-86-K0171. This research was partially done during our stay at Institut de Recherche en Informatique et Systemes Aleatoires (IRISA), Rennes, France, and the second author was also supported by IRISA during this time. 2 Laboratory for Information and Decision Systems, MIT, Cambridge, MA 02139.