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doc: minor correction
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src/controller/transcription.jl

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@@ -128,10 +128,11 @@ end
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Construct an orthogonal collocation on finite elements [`TranscriptionMethod`](@ref).
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Also known as pseudo-spectral method. The `h` argument is the hold order for ``\mathbf{u}``,
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and `no` argument, the number of collocation points ``n_o``. Only zero-order hold is
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currently implemented, so `h` must be `0`. The decision variable is similar to
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[`MultipleShooting`](@ref), but it also includes the collocation points:
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Also known as pseudo-spectral method. It supports continuous-time [`NonLinModel`](@ref)s
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only. The `h` argument is the hold order for ``\mathbf{u}``, and `no` argument, the number
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of collocation points ``n_o``. Only zero-order hold is currently implemented, so `h` must
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be `0`. The decision variable is similar to [`MultipleShooting`](@ref), but it also includes
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the collocation points:
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```math
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\mathbf{Z} = \begin{bmatrix} \mathbf{ΔU} \\ \mathbf{X̂_0} \\ \mathbf{K} \end{bmatrix}
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```
@@ -1012,7 +1013,7 @@ It warm-starts the solver at:
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```
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where ``\mathbf{x̂_0}(k+j|k-1)`` is the predicted state for time ``k+j`` computed at the
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last control period ``k-1``, expressed as a deviation from the operating point
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``\mathbf{x̂_{op}}``. The vector ``\mathbf{k}(k+j|k-1) include the ``n_o`` intermediate
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``\mathbf{x̂_{op}}``. The vector ``\mathbf{k}(k+j|k-1)`` include the ``n_o`` intermediate
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stage predictions for the interval ``k+j``, and is also computed at the last control period.
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"""
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function set_warmstart!(
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```
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for ``j = 0, 1, ... , H_p-1``, and knowing that the ``\mathbf{k}_o(k+j)`` vectors are
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extracted from the decision variable `Z̃`. The ``\mathbf{x_0}`` vectors are the
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deterministic state extracted from `Z̃`. The ``\mathbf{k̇}_o`` vector for the ``o``th
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deterministic state extracted from `Z̃`. The ``\mathbf{k̇}_o`` derivative for the ``o``th
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collocation point is computed from the continuous-time function `model.f!` and:
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```math
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\mathbf{k̇}_o(k+j) = \mathbf{f}\Big(\mathbf{k_o}(k+j), \mathbf{û_0}(k+j), \mathbf{d̂_0}(k+j), \mathbf{p}\Big)
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\mathbf{k̇}_o(k+j) = \mathbf{f}\Big(\mathbf{k}_o(k+j), \mathbf{û_0}(k+j), \mathbf{d̂_0}(k+j), \mathbf{p}\Big)
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```
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The disturbed input ``\mathbf{û_0}(k+j)`` is defined in [`f̂_input!`](@ref). The defects for
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the stochastic states ``\mathbf{s_s}`` are computed

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