Rigid-profile input scheduling under constrained dynamics with a water network application

TL;DR

This paper develops a method for scheduling rigid-profile water flow requests in open-channel networks, addressing non-convex optimization challenges with discretization and refinement techniques, validated through irrigation simulations.

Contribution

It introduces a novel discretization and refinement approach for non-convex semi-infinite programming in water network scheduling problems.

Findings

Effective discretization improves solution feasibility.

Refinement techniques enhance cost optimization.

Simulation confirms applicability to irrigation channels.

Abstract

The motivation for this work stems from the problem of scheduling requests for flow at supply points along an automated network of open-water channels. The off-take flows are rigid-profile inputs to the system dynamics. In particular, the channel operator can only shift orders in time to satisfy constraints on the automatic response to changes in the load. This leads to a non-convex semi-infinite programming problem, with sum-separable cost that encodes the collective sensitivity of end users to scheduling delays. The constraints encode the linear time-invariant continuous-time dynamics and limits on the state across a \al{continuous} scheduling horizon. Discretization is used to arrive at a more manageable approximation of the semi-infinite program. A method for parsimoniously refining the discretization is applied to ensure continuous-time feasibility for solutions of the approximate problem. It is then shown how to improve cost without loss of feasibility. Supporting analysis is provided, along with simulation results for a realistic irrigation channel setup to illustrate the approach.