added support for integrating LinModel in initstate!

Author: franckgaga

.vscode/settings.json

@@ -36,6 +36,7 @@
         "mathrm",
         "moveinput",
         "OSQP",
+        "Penrose",
         "Plamondon",
         "quadprog",
         "repeatdiag",

src/sim_model.jl

@@ -214,10 +214,11 @@ Omitting the operating points, the method evaluates the equilibrium ``\mathbf{x}
     \mathbf{x}(∞) = \mathbf{(I - A)^{-1}(B_u u + B_d d)}
 ```
 with the manipulated inputs held constant at ``\mathbf{u}`` and, the measured disturbances, 
-at ``\mathbf{d}``.
+at ``\mathbf{d}``. The Moore-Penrose pseudo-inverse evaluates ``\mathbf{(I - A)^{-1}``
+to support integrating `model` (integrator states will be 0).
 """
 function steadystate(model::LinModel, u, d=Float64[])
-    return (I - model.A) \ (model.Bu*(u - model.uop) + model.Bd*(d - model.dop))
+    return pinv(I - model.A)*(model.Bu*(u - model.uop) + model.Bd*(d - model.dop))
 end
 
 

src/state_estim.jl

@@ -170,9 +170,8 @@ Init `estim.x̂` states from current inputs `u`, measured outputs `ym` and distu
 
 The method tries to find a good steady-state to initialize `estim.x̂` estimate :
 
-- If `estim.model` is a non-integrating [`LinModel`](@ref), it evaluates `estim.model` 
-  steady-state with current inputs `u` and measured disturbances `d`, and saves the result 
-  to `estim.x̂[1:nx].`
+- If `estim.model` is a [`LinModel`](@ref), it evaluates `estim.model` steady-state with 
+  current inputs `u` and measured disturbances `d`, and saves the result to `estim.x̂[1:nx].`
 - Else, the current deterministic states `estim.x̂[1:nx]` are left unchanged (use 
   [`setstate!`](@ref) to manually modify them). 
   
@@ -198,7 +197,7 @@ function initstate!(estim::StateEstimator, u, ym, d=Float64[])
     model = estim.model
     # --- deterministic model states ---
     x̂d = estim.x̂[1:model.nx]
-    if isa(model, LinModel) && !any(abs.(eigvals(model.A)) .≈ 1)# non-integrating model only
+    if isa(model, LinModel)
         # init deterministic state with steady-states at current input and disturbance :
         x̂d = steadystate(model, u, d)
     end

test/runtests.jl

@@ -22,4 +22,4 @@ DocMeta.setdocmeta!(
 doctest(ModelPredictiveControl, testset="DocTest")
 
 
-end;
+end