A framework for state attraction of discrete event systems under partial observation

Abstract

State attraction for discrete event systems (DES) addresses the problem of reaching a desired subset of the plant state space after a bounded number of event occurrences. The problem of state attraction arises for example in fault-tolerant supervisory control or in the control of reconfigurable manufacturing systems, and is also applicable to systems biological problems such as the control of gene regulatory networks.

State attraction is investigated with the assumption of full event observation in the existing literature. This paper extends the concept of state attraction to the case of partial observation. The notion of weak attraction under partial observation (WAPO) is introduced and necessary and sufficient conditions for the existence of a supervisor under partial observation that achieves WAPO are derived. Furthermore, a solution algorithm is proposed that finds such supervisor whenever it exists. It is shown that such supervisor can always be realized as a subautomaton of the observer automaton of the DES plant. An application example from systems biology illustrates the obtained results.