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doc: detail in LinMPC
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src/controller/linmpc.jl

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@@ -137,10 +137,11 @@ Time-varying and non-diagonal weights are also supported. Modify the last block
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``\mathbf{Z}`` depends on the chosen [`TranscriptionMethod`](@ref) (default to
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[`SingleShooting`](@ref), hence ``\mathbf{Z = ΔU}``). The ``\mathbf{ΔU}`` includes the input
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increments ``\mathbf{Δu}(k+j) = \mathbf{u}(k+j) - \mathbf{u}(k+j-1)`` from ``j=0`` to
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``H_c-1``, the ``\mathbf{Ŷ}`` vector, the output predictions ``\mathbf{ŷ}(k+j)`` from
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``j=1`` to ``H_p``, and the ``\mathbf{U}`` vector, the manipulated inputs ``\mathbf{u}(k+j)``
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from ``j=0`` to ``H_p-1``. The slack variable ``ϵ`` relaxes the constraints, as described
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in [`setconstraint!`](@ref) documentation. See Extended Help for a detailed nomenclature.
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``H_c-1`` (without any custom move blocking), the ``\mathbf{Ŷ}`` vector, the output
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predictions ``\mathbf{ŷ}(k+j)`` from ``j=1`` to ``H_p``, and the ``\mathbf{U}`` vector, the
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manipulated inputs ``\mathbf{u}(k+j)`` from ``j=0`` to ``H_p-1``. The slack variable ``ϵ``
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relaxes the constraints, as described in [`setconstraint!`](@ref) documentation. See
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Extended Help for a detailed nomenclature.
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This method uses the default state estimator, a [`SteadyKalmanFilter`](@ref) with default
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arguments. This controller allocates memory at each time step for the optimization.

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