doc: minor modification

Author: franckgaga

src/controller/nonlinmpc.jl

@@ -126,7 +126,8 @@ the manipulated inputs, the predicted outputs and measured disturbances from ``k
 ```
 since ``H_c ≤ H_p`` implies that ``\mathbf{Δu}(k+H_p) = \mathbf{0}`` or ``\mathbf{u}(k+H_p)=
 \mathbf{u}(k+H_p-1)``. The vector ``\mathbf{D̂}`` includes the predicted measured disturbance
-over ``H_p``. The argument ``\mathbf{p}`` is a custom parameter object of any type.
+over ``H_p``. The argument ``\mathbf{p}`` is a custom parameter object of any type but use a
+mutable one if you want to modify it later e.g.: a vector.
 
 !!! tip
     Replace any of the 4 arguments with `_` if not needed (see `JE` default value below).

src/estimator/execute.jl

@@ -32,7 +32,8 @@ function returns the next state of the augmented model, defined as:
 ```
 where ``\mathbf{x̂_0}(k+1)`` is stored in `x̂next0` argument. The method mutates `x̂next0` and
 `û0` in place, the latter stores the input vector of the augmented model 
-``\mathbf{u_0 + ŷ_{s_u}}``.
+``\mathbf{u_0 + ŷ_{s_u}}``. The model parameter vector `model.p` is not included in the 
+function signature for conciseness.
 """
 function f̂!(x̂next0, û0, estim::StateEstimator, model::SimModel, x̂0, u0, d0)
     # `@views` macro avoid copies with matrix slice operator e.g. [a:b]

src/estimator/kalman.jl

@@ -582,7 +582,7 @@ See [`SteadyKalmanFilter`](@ref) for details on ``\mathbf{v}(k), \mathbf{w}(k)``
 \text{diag}(Q, Q_{int_u}, Q_{int_{ym}})}`` and ``\mathbf{R̂ = R}``. The functions
 ``\mathbf{f̂, ĥ}`` are `model` state-space functions augmented with the stochastic model of
 the unmeasured disturbances, which is specified by the numbers of integrator `nint_u` and
-`nint_ym` (see Extended Help). Model parameters ``\mathbf{p}`` are not an argument of
+`nint_ym` (see Extended Help). Model parameters ``\mathbf{p}`` are not argument of
 ``\mathbf{f̂, ĥ}`` functions for conciseness. The ``\mathbf{ĥ^m}`` function represents the
 measured outputs of ``\mathbf{ĥ}`` function (and unmeasured ones, for ``\mathbf{ĥ^u}``). The
 matrix ``\mathbf{P̂}`` is the estimation error covariance of `model` state augmented with the 

src/model/nonlinmodel.jl

@@ -67,10 +67,10 @@ functions are defined as:
     \mathbf{y}(t) &= \mathbf{h}\Big( \mathbf{x}(t), \mathbf{d}(t), \mathbf{p} \Big)
 \end{aligned}
 ```
-where ``\mathbf{x}``, ``\mathbf{y}, ``\mathbf{u}``, ``\mathbf{d}`` and ``\mathbf{p}`` are
-respectively the state, output, manipulated input, measured disturbance and parameter vectors,
-and ``t`` the time in second. If the dynamics is a function of time, simply add a measured
-disturbance defined as ``d(t)=t``. The functions can be implemented in two possible ways:
+where ``\mathbf{x}``, ``\mathbf{y}``, ``\mathbf{u}``, ``\mathbf{d}`` and ``\mathbf{p}`` are
+respectively the state, output, manipulated input, measured disturbance and parameter
+vectors. If the dynamics is a function of time, simply add a measured disturbance defined as
+``d(t) = t``. The functions can be implemented in two possible ways:
 
 1. **Non-mutating functions** (out-of-place): define them as `f(x, u, d, p) -> ẋ` and
    `h(x, d, p) -> y`. This syntax is simple and intuitive but it allocates more memory.
@@ -99,11 +99,11 @@ See also [`LinModel`](@ref).
 
 # Examples
 ```jldoctest
-julia> f!(ẋ, x, u, _ , _ ) = (ẋ .= -0.2x .+ u; nothing);
+julia> f!(ẋ, x, u, _ , p) = (ẋ .= p*x .+ u; nothing);
 
 julia> h!(y, x, _ , _ ) = (y .= 0.1x; nothing);
 
-julia> model1 = NonLinModel(f!, h!, 5.0, 1, 1, 1)               # continuous dynamics
+julia> model1 = NonLinModel(f!, h!, 5.0, 1, 1, 1, p=-0.2)       # continuous dynamics
 NonLinModel with a sample time Ts = 5.0 s, RungeKutta solver and:
  1 manipulated inputs u
  1 states x
@@ -127,8 +127,8 @@ NonLinModel with a sample time Ts = 2.0 s, empty solver and:
     State-space functions are similar for discrete dynamics:
     ```math
     \begin{aligned}
-        \mathbf{x}(k+1) &= \mathbf{f}\Big( \mathbf{x}(k), \mathbf{u}(k), \mathbf{d}(k), \mathbf{p}(k) \Big) \\
-        \mathbf{y}(k)   &= \mathbf{h}\Big( \mathbf{x}(k), \mathbf{d}(k), \mathbf{p}(k) \Big)
+        \mathbf{x}(k+1) &= \mathbf{f}\Big( \mathbf{x}(k), \mathbf{u}(k), \mathbf{d}(k), \mathbf{p} \Big) \\
+        \mathbf{y}(k)   &= \mathbf{h}\Big( \mathbf{x}(k), \mathbf{d}(k), \mathbf{p} \Big)
     \end{aligned}
     ```
     with two possible implementations as well: