starting moving horizon estimator

docs/src/public/predictive_control.md

@@ -78,7 +78,7 @@ NonLinMPC
 setconstraint!
 ```
 
-## Move Manipulated Input
+## Move Manipulated Input u
 
 ```@docs
 moveinput!

src/estimator/mhe.jl

@@ -0,0 +1,93 @@
+struct NonLinMHE{M<:SimModel} <: StateEstimator
+    model::M
+    optim::JuMP.Model
+    lastu0::Vector{Float64}
+    x̂::Vector{Float64}
+    P̂::Hermitian{Float64, Matrix{Float64}}
+    i_ym::Vector{Int}
+    nx̂::Int
+    nym::Int
+    nyu::Int
+    nxs::Int
+    As::Matrix{Float64}
+    Cs::Matrix{Float64}
+    nint_ym::Vector{Int}
+    P̂0::Hermitian{Float64, Matrix{Float64}}
+    Q̂::Hermitian{Float64, Matrix{Float64}}
+    R̂::Hermitian{Float64, Matrix{Float64}}
+    He::Int 
+    X̂max::Vector{Float64}
+    X̂min::Vector{Float64}
+    function NonLinMHE{M}(model::M, i_ym, nint_ym, P̂0, Q̂, R̂, He) where {M<:SimModel}
+        nu, nx, ny = model.nu, model.nx, model.ny
+        nym, nyu = length(i_ym), ny - length(i_ym)
+        Asm, Csm, nint_ym = init_estimstoch(i_ym, nint_ym)
+        nxs = size(Asm,1)
+        nx̂ = nx + nxs
+        validate_kfcov(nym, nx̂, Q̂, R̂, P̂0)
+        As, _ , Cs, _  = stoch_ym2y(model, i_ym, Asm, [], Csm, [])
+        nσ, γ, m̂, Ŝ = init_mhe(nx̂, He)
+        i_ym = collect(i_ym)
+        lastu0 = zeros(nu)
+        x̂ = [zeros(model.nx); zeros(nxs)]
+        P̂0 = Hermitian(P̂0, :L)
+        Q̂ = Hermitian(Q̂, :L)
+        R̂ = Hermitian(R̂, :L)
+        P̂ = copy(P̂0)
+        return new(
+            model,
+            lastu0, x̂, P̂, 
+            i_ym, nx̂, nym, nyu, nxs, 
+            As, Cs, nint_ym,
+            P̂0, Q̂, R̂,
+            nσ, γ, m̂, Ŝ
+        )
+    end
+end
+
+@doc raw"""
+    NonLinMHE(model::SimModel; <keyword arguments>)
+
+Construct a nonlinear moving horizon estimator with the [`SimModel`](@ref) `model`.
+
+Both [`LinModel`](@ref) and [`NonLinModel`](@ref) are supported. The process model is 
+identical to [`UnscentedKalmanFilter`](@ref).
+
+# Arguments
+- `model::SimModel` : (deterministic) model for the estimations.
+- `He::Int=10` : estimation horizon.
+- `<keyword arguments>` of [`SteadyKalmanFilter`](@ref) constructor.
+- `<keyword arguments>` of [`KalmanFilter`](@ref) constructor.
+
+# Examples
+```jldoctest
+julia> model = NonLinModel((x,u,_)->0.1x+u, (x,_)->2x, 10.0, 1, 1, 1);
+
+```
+"""
+function NonLinMHE(
+    model::M;
+    i_ym::IntRangeOrVector = 1:model.ny,
+    σP0::Vector = fill(1/model.nx, model.nx),
+    σQ::Vector  = fill(1/model.nx, model.nx),
+    σR::Vector  = fill(1, length(i_ym)),
+    nint_ym::IntVectorOrInt = fill(1, length(i_ym)),
+    σP0_int::Vector = fill(1, max(sum(nint_ym), 0)),
+    σQ_int::Vector  = fill(1, max(sum(nint_ym), 0)),
+    He::Int = 10
+) where {M<:SimModel}
+    # estimated covariances matrices (variance = σ²) :
+    P̂0 = Diagonal{Float64}([σP0  ; σP0_int   ].^2);
+    Q̂  = Diagonal{Float64}([σQ   ; σQ_int    ].^2);
+    R̂  = Diagonal{Float64}(σR.^2);
+    return NonLinMHE{M}(model, i_ym, nint_ym, P̂0, Q̂ , R̂, He)
+end
+
+@doc raw"""
+    NonLinMHE{M<:SimModel}(model::M, i_ym, nint_ym, P̂0, Q̂, R̂, He)
+
+Construct the estimator from the augmented covariance matrices `P̂0`, `Q̂` and `R̂`.
+
+This syntax allows nonzero off-diagonal elements in ``\mathbf{P̂}_{-1}(0), \mathbf{Q̂, R̂}``.
+"""
+NonLinMHE{M}(model::M, i_ym, nint_ym, P̂0, Q̂, R̂, He) where {M<:SimModel}