table for predictive control nomenclature

Author: franckgaga

src/predictive_control.jl

@@ -146,24 +146,35 @@ Construct a linear predictive controller `LinMPC` based on [`LinModel`](@ref) `m
 
 The controller minimizes the following objective function at each discrete time ``k``:
 ```math
-\min_{\mathbf{ΔU}, ϵ}   \mathbf{(R̂_y - Ŷ)}' \mathbf{M}_{H_p} \mathbf{(R̂_y - Ŷ)}  + 
-                             \mathbf{(ΔU)}' \mathbf{N}_{H_c} \mathbf{(ΔU)}  +
-                        \mathbf{(R̂_u - U)}' \mathbf{L}_{H_p} \mathbf{(R̂_u - U)}  + Cϵ^2
+\min_{\mathbf{ΔU}, ϵ}    \mathbf{(R̂_y - Ŷ)}' \mathbf{M}_{H_p} \mathbf{(R̂_y - Ŷ)}   
+                       + \mathbf{(ΔU)}'      \mathbf{N}_{H_c} \mathbf{(ΔU)}  
+                       + \mathbf{(R̂_u - U)}' \mathbf{L}_{H_p} \mathbf{(R̂_u - U)} 
+                       + C ϵ^2
 ```
-in which :
-
-- ``H_p`` : prediction horizon 
-- ``H_c`` : control horizon
-- ``\mathbf{ΔU}`` : manipulated input increments over ``H_c``
-- ``\mathbf{Ŷ}`` : predicted outputs over ``H_p``
-- ``\mathbf{U}`` : manipulated inputs over ``H_p``
-- ``\mathbf{R̂_y}`` : predicted output setpoints over ``H_p``
-- ``\mathbf{R̂_u}`` : predicted manipulated input setpoints over ``H_p``
-- ``\mathbf{M}_{H_p} = \text{diag}\mathbf{(M,M,...,M)}`` : output setpoint tracking weights
-- ``\mathbf{N}_{H_c} = \text{diag}\mathbf{(N,N,...,N)}`` : manipulated input increment weights
-- ``\mathbf{L}_{H_p} = \text{diag}\mathbf{(L,L,...,L)}`` : manipulated input setpoint tracking weights
-- ``C`` : slack variable weight
-- ``ϵ`` : slack variable for constraint softening
+in which the weight matrices are :
+```math
+\begin{aligned}
+    \mathbf{M}_{H_p} &= \text{diag}\mathbf{(M,M,...,M)}     \\
+    \mathbf{N}_{H_c} &= \text{diag}\mathbf{(N,N,...,N)}     \\
+    \mathbf{L}_{H_p} &= \text{diag}\mathbf{(L,L,...,L)}     
+\end{aligned}
+```
+and following the nomeclature:
+
+| Var.                 | Description                                        |
+| :------------------- | :------------------------------------------------- |
+| ``H_p``              | prediction horizon                                 |
+| ``H_c``              | control horizon                                    |
+| ``\mathbf{ΔU}``      | manipulated input increments over ``H_c``          |
+| ``\mathbf{Ŷ}``       | predicted outputs over ``H_p``                     |
+| ``\mathbf{U}``       | manipulated inputs over ``H_p``                    |
+| ``\mathbf{R̂_y}``     | predicted output setpoints over ``H_p``            |
+| ``\mathbf{R̂_u}``     | predicted manipulated input setpoints over ``H_p`` |
+| ``\mathbf{M}_{H_p}`` | output setpoint tracking weights                   |
+| ``\mathbf{N}_{H_c}`` | manipulated input increment weights                |
+| ``\mathbf{L}_{H_p}`` | manipulated input setpoint tracking weights        |
+| ``C``                | slack variable weight                              |
+| ``ϵ``                | slack variable for constraint softening            |
 
 The ``\mathbf{ΔU}`` vector includes the manipulated input increments ``\mathbf{Δu}(k+j) = 
 \mathbf{u}(k+j) - \mathbf{u}(k+j-1)`` from ``j=0`` to ``H_c-1``, the ``\mathbf{Ŷ}`` vector,