add files

Author: ocots

test/ctdirect/problems/beam2.jl

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+# Beam example from bocop
+# beam2: coordinate wise dynamics
+
+function beam2()
+    beam2 = @def begin
+        t ∈ [0, 1], time
+        x ∈ R², state
+        u ∈ R, control
+        x(0) == [0, 1]
+        x(1) == [0, -1]
+        ∂(x₁)(t) == x₂(t)
+        ∂(x₂)(t) == u(t)
+        0 ≤ x₁(t) ≤ 0.1
+        -10 ≤ u(t) ≤ 10
+        ∫(u(t)^2) → min
+    end
+
+    return ((ocp=beam2, obj=8.898598, name="beam2", init=nothing))
+end

test/ctdirect/suite/test_exa.jl

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+# beam2
+if !isdefined(Main, :beam2)
+    include("../problems/beam2.jl")
+end
+
+display = false # during optim solves
+
+# Test on CPU
+
+println("testing: ExaModels (CPU)")
+
+@testset verbose = true showtiming = true ":examodel :cpu :trapeze" begin
+    prob = beam2()
+    sol = solve(prob.ocp, :madnlp, :exa; disc_method = :trapeze, display = display)
+    @test sol.objective ≈ prob.obj rtol = 1e-2
+end
+
+@testset verbose = true showtiming = true ":examodel :cpu :euler :init" begin
+    prob = beam2()
+    sol = solve(prob.ocp, :madnlp, :exa; disc_method = :euler, display = display, init=(control=6.66,), max_iter = 0)
+    @test control(sol)(0.5) == 6.66
+end