Bug tf variable #189
Description
It seems that this is not correct:
julia> @def ocp begin
tf ∈ R, variable
t ∈ [0, tf], time
x ∈ R, state
u ∈ R, control
ẋ(t) == tf * u(t)
x(0) == 0
x(tf) == 1
tf + 0.5∫(u(t)^2) → min
end
The (autonomous) optimal control problem is given by:
tf ∈ R, variable
t ∈ [0, tf], time
x ∈ R, state
u ∈ R, control
ẋ(t) == tf * u(t)
x(0) == 0
x(tf) == 1
tf + 0.5 * ∫(u(t) ^ 2) → min
The (autonomous) optimal control problem is of the form:
minimize J(x, u, tf) = g(x(0), x(tf), tf) + ∫ f⁰(x(t), u(t), tf) dt, over [0, tf]
subject to
ẋ(t) = f(x(t), u(t), tf), t in [0, tf] a.e.,
ϕl ≤ ϕ(x(0), x(tf), tf) ≤ ϕu,
where x(t) ∈ R, u(t) ∈ R and tf ∈ R.
Declarations (* required):
╭────────┬────────┬──────────┬──────────┬───────────┬────────────┬─────────────╮
│ times* │ state* │ control* │ variable │ dynamics* │ objective* │ constraints │
├────────┼────────┼──────────┼──────────┼───────────┼────────────┼─────────────┤
│ V │ V │ V │ V │ V │ V │ V │
╰────────┴────────┴──────────┴──────────┴───────────┴────────────┴─────────────╯
julia> sol = solve(ocp)
This is Ipopt version 3.14.16, running with linear solver MUMPS 5.7.3.
Number of nonzeros in equality constraint Jacobian...: 1003
Number of nonzeros in inequality constraint Jacobian.: 0
Number of nonzeros in Lagrangian Hessian.............: 203
Total number of variables............................: 304
variables with only lower bounds: 0
variables with lower and upper bounds: 0
variables with only upper bounds: 0
Total number of equality constraints.................: 203
Total number of inequality constraints...............: 0
inequality constraints with only lower bounds: 0
inequality constraints with lower and upper bounds: 0
inequality constraints with only upper bounds: 0
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
0 2.0000000e-01 9.00e-01 4.91e-03 0.0 0.00e+00 - 0.00e+00 0.00e+00 0
1 2.3319855e-01 8.99e-01 3.84e-01 -11.0 3.36e+01 - 1.00e+00 9.77e-04h 11
2 3.1063422e-01 8.96e-01 1.15e+00 -11.0 1.94e+01 - 1.00e+00 3.91e-03h 9
3 5.7872626e-01 8.82e-01 1.03e+00 -11.0 1.74e+01 -2.0 1.00e+00 1.56e-02h 7
4 8.6337333e-01 8.68e-01 7.24e-01 -11.0 1.83e+01 -0.7 1.00e+00 1.56e-02h 7
5 1.2396253e+00 8.14e-01 1.02e+00 -11.0 6.07e+00 - 1.00e+00 6.25e-02h 5
6 8.3728076e-01 7.10e-03 4.56e+00 -11.0 9.76e-01 -1.1 1.00e+00 1.00e+00h 1
7 1.6241923e+00 1.05e-02 6.93e+00 -11.0 1.43e+00 - 1.00e+00 1.00e+00h 1
8 1.5839909e+00 2.95e-04 6.23e-01 -11.0 1.00e-01 -0.7 1.00e+00 1.00e+00h 1
9 1.2672905e+00 1.12e-02 4.91e-01 -11.0 1.95e+00 - 1.00e+00 1.00e+00f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
10 1.3583706e+00 2.54e-03 3.59e-03 -11.0 6.11e-01 - 1.00e+00 1.00e+00h 1
11 1.4778821e+00 1.13e-04 9.96e-03 -11.0 9.02e-02 - 1.00e+00 1.00e+00h 1
12 1.4755675e+00 1.90e-07 1.54e-06 -11.0 4.38e-03 - 1.00e+00 1.00e+00h 1
13 1.4755759e+00 5.11e-12 2.99e-10 -11.0 2.27e-05 - 1.00e+00 1.00e+00h 1
Number of Iterations....: 13
(scaled) (unscaled)
Objective...............: 1.4755758928406426e+00 1.4755758928406426e+00
Dual infeasibility......: 2.9935254275414991e-10 2.9935254275414991e-10
Constraint violation....: 5.1116888499791457e-12 5.1116888499791457e-12
Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+00
Complementarity.........: 0.0000000000000000e+00 0.0000000000000000e+00
Overall NLP error.......: 2.9935254275414991e-10 2.9935254275414991e-10
Number of objective function evaluations = 47
Number of objective gradient evaluations = 14
Number of equality constraint evaluations = 53
Number of inequality constraint evaluations = 0
Number of equality constraint Jacobian evaluations = 14
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations = 13
Total seconds in IPOPT = 0.190
EXIT: Optimal Solution Found.
CTBase.OptimalControlSolution
julia> p0 = sol.costate(0)
0.7377879463735035
julia> tf = sol.variable
1.1066819197577107