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hi @oameye (cc @ocots @PierreMartinon); moving your separate example here (different issue compared to #369). The example below converges with the commented version of the cost, not with the uncommented one (which is not exactly what you posted), but runs without any AD error:
- can you please confirm which (new) cost you want to minimise?
- in any case, I suggest to replace your
mysqrtby theasqrtfunction below (smoothed and symmetrised)
using OptimalControl
using NLPModelsIpopt
using LinearAlgebra
T = 50 # Time horizon
# Define the vector field
f(u, v) = [u - u^3 - 10*u*v^2, -(1 - u^2)*v]
f(x) = f(x...)
asqrt(x; ε=1e-9) = sqrt(sqrt(x^2 + ε^2))
@def action begin
t ∈ [0, T], time
x ∈ R², state
u ∈ R², control
x(0) == [-1, 0] # Starting point (left well)
x(T) == [1, 0] # End point (right well)
ẋ(t) == u(t) # Path dynamics
#∫( sum((u(t) - f(x(t))).^2) ) → min # Minimize deviation from deterministic flow
∫( asqrt(sum((u(t) - f(x(t))).^2)) ) → min # Minimize deviation from deterministic flow
end
# Linear interpolation for x₁
x1(t) = -(1 - t/T) + t/T
# Parabolic guess for x₂
x2(t) = 0.3(-x1(t)^2 + 1)
x(t) = [x1(t), x2(t)]
u(t) = f(x(t))
init = (state=x, control=u)
sol = solve(action; init=init, grid_size=50)