Trajectories

The primal part of a solution is read through accessors that return callables of time (interpolated from the stored samples) for the trajectories, and plain values for the variable and the objective.

Accessor	Returns	Shape
state	x(t)	callable →
control	u(t)	callable →
costate	p(t)	callable →
variable	v	value
objective	optimal cost	scalar

using CTModels

pre = CTModels.PreModel()
CTModels.variable!(pre, 1, "v")
CTModels.time!(pre; t0=0.0, tf=1.0)
CTModels.state!(pre, 2)
CTModels.control!(pre, 1)
CTModels.dynamics!(pre, (r, t, x, u, v) -> (r[1] = x[2]; r[2] = u[1]; nothing))
CTModels.objective!(pre, :min; lagrange=(t, x, u, v) -> 0.5u[1]^2)
CTModels.time_dependence!(pre; autonomous=true)
ocp = CTModels.build(pre)

N = 101
T = collect(range(0.0, 1.0; length=N))
X = hcat(cos.(T), -sin.(T))
U = reshape(-cos.(T), N, 1)
P = zeros(N, 2)
v = [2.0]                         # the optimisation variable value

sol = CTModels.build_solution(ocp, T, X, U, v, P;
    objective=0.5, iterations=10, constraints_violation=1e-9,
    message="ok", status=:optimal, successful=true)

Reading trajectories

The trajectories are callables, so they can be evaluated at any time in the interval, not only at grid points — the samples are interpolated:

x = CTModels.state(sol)
u = CTModels.control(sol)
p = CTModels.costate(sol)

julia> x(0.0)
2-element Vector{Float64}:
  1.0
 -0.0

julia> x(0.123)
2-element Vector{Float64}:
  0.9924346132121428
 -0.12268878788815202

julia> u(0.5)
-0.8775825618903728

julia> p(1.0)
2-element Vector{Float64}:
 0.0
 0.0

julia> CTModels.variable(sol)
2.0

julia> CTModels.objective(sol)
0.5

Interpolation of the control

State and costate are interpolated linearly. The control may instead be piecewise constant — typical of direct collocation — selected by the control_interpolation keyword of build_solution (:linear or :constant). The choice is recorded and read back with control_interpolation:

sol_const = CTModels.build_solution(ocp, T, X, U, v, P;
    objective=0.5, iterations=10, constraints_violation=1e-9,
    message="ok", status=:optimal, successful=true,
    control_interpolation=:constant)

julia> CTModels.control_interpolation(sol)
:constant

julia> CTModels.control_interpolation(sol_const)
:constant

Because the interpolation kind is a stored field — not baked into an opaque closure — downstream code (plotting, serialization) can branch on it explicitly. The Duals & diagnostics page covers the remaining accessors.