Informing the allocation algorithm about purely physical flows (MPC v0)

[SouthEndMusic]

We came to the conclusion with @FaridAlavi that (basic) model predictive control could help us resolve the problem that the allocation algorithm does not currently take purely physical flows into account. These can reduce the amount of available water for the algorithm to divide, but the algorithm currently doesn't 'see' this flow because the algorithm only computes flows based on demands.

The formulation to use (with one UserDemand $U$, a bucket volume $V$ and a physical outflow $f(V)$ would be:

$$ V(t_{n+1}) = V(t_n) -f(V(t_n))-U(t_n) $$

extensible into the MPC paradigm,

$$ V(t_{n+2})=V(t_{n+1}) -f(V(t_{n+1}))-U(t_{n+1}) $$

[gijsber]

As discussed with Farid