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starting init_predmat modifications for multiple shooting
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franckgaga committed Feb 2, 2025
1 parent c7d7dc8 commit fa386ac
Showing 1 changed file with 6 additions and 6 deletions.
12 changes: 6 additions & 6 deletions src/controller/construct.jl
Original file line number Diff line number Diff line change
Expand Up @@ -515,10 +515,10 @@ Construct the prediction matrices for [`LinModel`](@ref) `model`.
The model predictions are evaluated from the deviation vectors (see [`setop!`](@ref)) and:
```math
\begin{aligned}
\mathbf{Ŷ_0} &= \mathbf{E ΔU} + \mathbf{G d_0}(k) + \mathbf{J D̂_0}
+ \mathbf{K x̂_0}(k) + \mathbf{V u_0}(k-1)
+ \mathbf{B} + \mathbf{Ŷ_s} \\
&= \mathbf{E ΔU} + \mathbf{F}
\mathbf{Ŷ_0} &= \mathbf{E Z} + \mathbf{G d_0}(k) + \mathbf{J D̂_0}
+ \mathbf{K x̂_0}(k) + \mathbf{V u_0}(k-1)
+ \mathbf{B} + \mathbf{Ŷ_s} \\
&= \mathbf{E Z} + \mathbf{F}
\end{aligned}
```
in which ``\mathbf{x̂_0}(k) = \mathbf{x̂}_i(k) - \mathbf{x̂_{op}}``, with ``i = k`` if
Expand All @@ -533,10 +533,10 @@ stochastic predictions ``\mathbf{Ŷ_s=0}`` if `estim` is not a [`InternalModel`
terminal states at ``k+H_p``:
```math
\begin{aligned}
\mathbf{x̂_0}(k+H_p) &= \mathbf{e_x̂ ΔU} + \mathbf{g_x̂ d_0}(k) + \mathbf{j_x̂ D̂_0}
\mathbf{x̂_0}(k+H_p) &= \mathbf{e_x̂ Z} + \mathbf{g_x̂ d_0}(k) + \mathbf{j_x̂ D̂_0}
+ \mathbf{k_x̂ x̂_0}(k) + \mathbf{v_x̂ u_0}(k-1)
+ \mathbf{b_x̂} \\
&= \mathbf{e_x̂ ΔU} + \mathbf{f_x̂}
&= \mathbf{e_x̂ Z} + \mathbf{f_x̂}
\end{aligned}
```
The matrices ``\mathbf{E, G, J, K, V, B, e_x̂, g_x̂, j_x̂, k_x̂, v_x̂, b_x̂}`` are defined in the
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