Knot-vectors?

[jbcaillau]

@PierreMartinon @gergaud Error when solving the problem

@def ocp begin
    tf ∈ R, variable
    t ∈ [ 0, tf ], time
    x ∈ R², state
    u ∈ R, control
    tf ≥ 0
    -1 ≤ u(t) ≤ 1
    q = x₁
    v = x₂
    q(0) == 1
    v(0) == 2
    q(tf) == 0
    v(tf) == 0
    0 ≤ q(t) ≤ 5
    -2 ≤ v(t) ≤ 3
    (u^2)(t) ≤ 100
    ẋ(t) == [ v(t), u(t) ]
    tf → min
end

NB. The constraint (u^2)(t) ≤ 100 is for testing purpose only

[PierreMartinon]

If I recall correctly the knot-vector message comes sometimes from the 1D interpolation when generating the (functional) OCP solution from the discretized problem solution. I did not find the cause when looking at the time steps vector that looked fine, but the problem vanished in the CTDirect test suite when updating to Julia 1.9 or more. I'll retest this.

[PierreMartinon]

Ok @jbcaillau , the solution generation fails here because the optimization did not converge, and finished with a negative tf. The time steps grid is therefore nonincreasing... I added a failsafe here to prevent the error: tf = max(tf, t0+eps).

On a side note, the optimization fails because the constraint tf>=0 causes Ipopt to get stuck at tf=0. Putting a strictly positive lower bound (eg 0.1) is enough to get the convergence. We may want to warn about this as it is a very common 'mistake' (in Bocop the lower bound was set automatically to 1e-3). I could try to detect a 0 lower bound for tf ?

[jbcaillau]

@PierreMartinon

Ok @jbcaillau , the solution generation fails here because the optimization did not converge, and finished with a negative tf. The time steps grid is therefore nonincreasing... I added a failsafe here to prevent the error: tf = max(tf, t0+eps).

PR?

On a side note, the optimization fails because the constraint tf>=0 causes Ipopt to get stuck at tf=0. Putting a strictly positive lower bound (eg 0.1) is enough to get the convergence. We may want to warn about this as it is a very common 'mistake' (in Bocop the lower bound was set automatically to 1e-3). I could try to detect a 0 lower bound for tf ?

Well done. Indeed, back to normal with $t_f \geq 0.3$:

@def ocp begin
           tf ∈ R, variable
           t ∈ [ 0, tf ], time
           x ∈ R², state
           u ∈ R, control
           tf ≥ 1e-3
           -1 ≤ u(t) ≤ 1
           q = x₁
           v = x₂
           q(0) == 1
           v(0) == 2
           q(tf) == 0
           v(tf) == 0
           0 ≤ q(t) ≤ 5
           -2 ≤ v(t) ≤ 3
           (u^2)(t) ≤ 100
           ẋ(t) == [ v(t), u(t) ]
           tf → min
       end

[PierreMartinon]

@jbcaillau #76