IEEE Transactions on Automatic Control 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. Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE 27 OCT 1989 2. REPORT TYPE 3. DATES COVERED 00-10-1989 to 00-10-1989 4. TITLE AND SUBTITLE Observability of Discrete Event Dynamic Systems 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Massachusetts Institute of Technology,Laboratory for Information and Decision Systems,77 Massachusetts Avenue,Cambridge,MA,02139-4307 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S) 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; distribution unlimited 13. SUPPLEMENTARY NOTES 14. ABSTRACT 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT 18. NUMBER OF PAGES 41 19a. NAME OF RESPONSIBLE PERSON a. REPORT unclassified b. ABSTRACT unclassified c. THIS PAGE unclassified Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18