Delay-Robustness for Localization-Based Distributed Control of Timed Discrete-Event Systems

This paper identifies properties of bounded and unbounded delay-robustness for distributed supervisory control for timed discrete-event systems (TDES) with communication delay. In our previous work, for untimed DES we have proposed an effective verification tool to identify delay-robustness for distributed controllers constructed by the supervisor localization procedure. Delay-robustness means that the overall system behavior controlled by distributed controllers with communication delay is equivalent to its delay-free counterpart. Further, determine delay-robustness to be bounded or unbounded by the standard controllability checking procedure. In this paper, we first apply the timed localization procedure to obtain a set of local controllers and tick preemptors; second, we model each inter-agent channel as a 2-state TDES in which the clock event tick is added to each state, and thus the time delay is represented by an exact number of ticks; third, we introduce the TDES delay-robustness. We distinguish bounded or unbounded delay-robustness of the system, and for those events identified as bounded delay-robust, we propose an algorithm to determine the maximal delay bound in terms of the number of tick events, rather than the number of untimed events that may occurred at random. Based on these studies, we present another algorithm to compute a set of maximal delay bounds for the communication events, under the condition that the overall system behavior with communication delay preserves the global optimality and nonblocking property. Our results are illustrated by the example of an up-load tap-changing transformer (ULTC).