@ocots @PierreMartinon values extracted from an :exa solution look wrong, as well as plots. same when solving with Ipopt or MadNLP. conversely everything is OK with Ipopt and MadNLP and :adnlp. optimisation looks OK as objective is correct (*). See:

using OptimalControl
using MadNLP
using Plots

o = @def begin
           t ∈ [0, 1], time
           x ∈ R², state
           u ∈ R, control
           x(0) == [-1, 0]
           x(1) == [0, 0]
           ∂(x₁)(t) == x₂(t)
           ∂(x₂)(t) == u(t)
           ∫( 0.5u(t)^2 ) → min
end

sol = solve(o, :exa, :madnlp)

plot(sol)

(*) on Goddard, for instance, the objective is OK so i believe everything goes fine until post analysis; then, the value of the free final time displayed by the pretty printer is wrong, as well as times, and then plots