We consider load scheduling on constrained continuous-time linear dynamicalsystems, such as automated irrigation and other distribution networks. Therequested loads are rigid, i.e., the shapes cannot be changed. Hence, it isonly possible to shift the order back-and-forth in time to arrive at a feasibleschedule. We present a numerical algorithm based on using log-barrier functionsto include the state constraints in the social cost function (i.e., anappropriate function of the scheduling delays). This algorithm requires afeasible initialization. Further, in another algorithm, we treat the stateconstraints as soft constraints and heavily penalize the constraint violations.This algorithm can even be initialized at an infeasible point. Theapplicability of both these numerical algorithms is demonstrated on anautomated irrigation network with two pools and six farms.
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