@@ -151,30 +151,30 @@ The controller minimizes the following objective function at each discrete time
151151 + \m athbf{(R̂_u - U)}' \m athbf{L}_{H_p} \m athbf{(R̂_u - U)}
152152 + C ϵ^2
153153```
154- in which the weight matrices are :
154+ in which the weight matrices are repeated ``H_p`` or ``H_c`` times :
155155```math
156156\b egin{aligned}
157157 \m athbf{M}_{H_p} &= \t ext{diag}\m athbf{(M,M,...,M)} \\
158158 \m athbf{N}_{H_c} &= \t ext{diag}\m athbf{(N,N,...,N)} \\
159159 \m athbf{L}_{H_p} &= \t ext{diag}\m athbf{(L,L,...,L)}
160160\e nd{aligned}
161161```
162- and following the nomeclature:
163-
164- | Var. | Description |
165- | :------------------- | :------------------------------------------------- |
166- | ``H_p`` | prediction horizon |
167- | ``H_c`` | control horizon |
168- | ``\m athbf{ΔU}`` | manipulated input increments over ``H_c`` |
169- | ``\m athbf{Ŷ}`` | predicted outputs over ``H_p`` |
170- | ``\m athbf{U}`` | manipulated inputs over ``H_p`` |
171- | ``\m athbf{R̂_y}`` | predicted output setpoints over ``H_p`` |
172- | ``\m athbf{R̂_u}`` | predicted manipulated input setpoints over ``H_p`` |
173- | ``\m athbf{M}_{H_p}`` | output setpoint tracking weights |
174- | ``\m athbf{N}_{H_c}`` | manipulated input increment weights |
175- | ``\m athbf{L}_{H_p}`` | manipulated input setpoint tracking weights |
176- | ``C`` | slack variable weight |
177- | ``ϵ`` | slack variable for constraint softening |
162+ and with the following nomeclature:
163+
164+ | Var. | Description |
165+ | :---------------- | :------------------------------------------------- |
166+ | ``H_p`` | prediction horizon |
167+ | ``H_c`` | control horizon |
168+ | ``\m athbf{ΔU}`` | manipulated input increments over ``H_c`` |
169+ | ``\m athbf{Ŷ}`` | predicted outputs over ``H_p`` |
170+ | ``\m athbf{U}`` | manipulated inputs over ``H_p`` |
171+ | ``\m athbf{R̂_y}`` | predicted output setpoints over ``H_p`` |
172+ | ``\m athbf{R̂_u}`` | predicted manipulated input setpoints over ``H_p`` |
173+ | ``\m athbf{M}`` | output setpoint tracking weights |
174+ | ``\m athbf{N}`` | manipulated input increment weights |
175+ | ``\m athbf{L}`` | manipulated input setpoint tracking weights |
176+ | ``C`` | slack variable weight |
177+ | ``ϵ`` | slack variable for constraint softening |
178178
179179The ``\m athbf{ΔU}`` vector includes the manipulated input increments ``\m athbf{Δu}(k+j) =
180180\m athbf{u}(k+j) - \m athbf{u}(k+j-1)`` from ``j=0`` to ``H_c-1``, the ``\m athbf{Ŷ}`` vector,
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