Build shifted variables in var_derivative! for discrete systems

[baggepinnen]

Summary

StateSelection.var_derivative!(::TearingState, ::Int) always builds the new variable as Differential(iv)(v). In a discrete system the variables are related by shifts, so the differential form is not recognized by the discrete reassembly. The method now builds simplify_shifts(Shift(iv, 1)(v)) when the structure is discrete.

Reproduction

eliminate_perfect_aliases! calls var_derivative! when a variable that is shifted in the system is eliminated in favour of an alias target that has no shifted form yet:

using ModelingToolkit
using ModelingToolkit: t_nounits as t
k = ShiftIndex(t)
@parameters p
@variables u(t) y(t) z(t)
@named sys = System([u ~ p, y ~ u(k - 1), z ~ y], t)
ss = mtkcompile(sys)
unknowns(ss)   # [y(t), yₜ₊₁(t)]
equations(ss)  # [Shift(t, 1)(y(t)) ~ yₜ₊₁(t)]
observed(ss)   # [Differential(t, 1)(y(t)) ~ p, z(t) ~ y(t), uₜ₋₁(t) ~ y(t)]

The alias z ~ y puts u (whose shifted form u(k + 1) is a variable of the system after shift_discrete_system) in the same alias group as y(k + 1) and z(k + 1). With y(k + 1) as the target, its shifted form is requested from var_derivative!, which returns Differential(t)(y). The compiled system then has two unknowns and one equation, and DiscreteProblem fails with "Equations (1), unknowns (2), and initial conditions (2) are of different lengths". With z ~ 2y in place of the alias the compile is correct, since no alias elimination takes place.

With this change the system compiles to the single unknown y with Shift(t, 1)(y) ~ yₜ₊₁, yₜ₊₁ ~ p, z ~ y and uₜ₋₁ ~ y.

This is the structure of every model that uses a one-sample delay whose output is connected to another block, such as DiscreteComponents.UnitDelay; it was found while running linearize_hybrid of SciML/ModelingToolkit.jl#5173 over the DiscreteComponents examples (finding 3 of this comment).

Tests

A regression test in lib/ModelingToolkitTearing/test/runtests.jl compiles the model above, checks that a single unknown remains and that no Differential appears in the equations or observed equations, and checks the values of y and z after the first tick of a DiscreteProblem. The discrete_system, implicit_discrete_system and clock tests of ModelingToolkit pass with this change.

🤖 Generated with Claude Code

https://claude.ai/code/session_01QBgBrXDidWG1G2KF64gAte