On Expected Value Strong Controllability

The Probabilistic Simple Temporal Network (PSTN) generalizes Simple Temporal Networks with Uncertainty (STNUs) by introducing probability distributions over the timing of uncontrollable timepoints. PSTNs are controllable if there is a strategy to execute the controllable timepoints while bounding the risk of violating any constraint to a small value. If this risk bound can't be satisfied, PSTNs are not considered controllable. We introduce the Expected Value Probabilistic SimpleTemporal Network (EPSTN), which extends PSTNs by including a benefit to the satisfaction of temporal constraints. We study the problem of Expected Value Strong Controllability (EvSC) of EPSTNs, which seeks a schedule maximizing the expected value of satisfied constraints. We solve the EvSC problem by extending a previously developed linear program, combined with search over constraints to violate at execution time. We describe conditions under which the solution to this linear program is the maximum expected value schedule. We then show how to search for constraints to discard, using the linear program at the core of the search. While the general problem is shown to be exponential, we conclude by providing several methods to bound the complexity of search.