Tracking and Restrictability in Discrete Event Dynamic Systems
Cüneyt M. Özveren, Alan S. Willsky · SIAM Journal on Control and Optimization · 1992
This paper formulates and analyzes notions of tracking and restrictability for discrete event dynamic systems (DEDS). The DEDS model used is a finite-state automaton in which there is control over some events. A second set of events, called the set of tracking events, is also specified, and the tracking problem is one of constructing a compensator so that the tracking event trajectory of the closed loop system follows a given string exactly. This problem is analyzed in detail and, in particular, a characterization of all trackable strings is characterized. The related notion of restrictability is analyzed in which the closed-loop system is required to generate tracking event strings in a given desired language. A relaxed version of this concept is also analyzed, allowing an initial transient before desired language tracking is achieved. Finally, a notion of reliability is introduced and analyzed, which allows for testing if the system can recover from errors in a finite number of transitions, and algorithms are presented for constructing compensators for reliable restrictability. A manufacturing system example is used to motivate and illustrate the problems considered and results obtained.