Scheduling Rigid Demands on Continuous-Time Linear Shift-Invariant Systems

TL;DR

This paper develops numerical algorithms for scheduling rigid loads in continuous-time linear systems, ensuring feasibility either through feasible initialization or penalization, demonstrated on an irrigation network.

Contribution

It introduces two novel algorithms for load scheduling with rigid demands, handling both feasible and infeasible initial conditions in continuous-time systems.

Findings

Algorithms successfully schedule loads in irrigation network

Log-barrier method enforces state constraints effectively

Penalty-based method handles infeasible initial points

Abstract

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