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doc: replace urls with inter-links
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docs/src/manual/mtk.md

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## Pendulum Model
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This example integrates the simple pendulum model of the [last section](@ref man_nonlin) in the
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[`ModelingToolkit.jl`](https://docs.sciml.ai/ModelingToolkit/stable/) (MTK) framework and
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This example integrates the simple pendulum model of the [last section](@ref man_nonlin) in
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[`ModelingToolkit`](https://docs.sciml.ai/ModelingToolkit/stable/) (MTK) framework and
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extracts appropriate `f!` and `h!` functions to construct a [`NonLinModel`](@ref). An
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[`NonLinMPC`](@ref) is designed from this model and simulated to reproduce the results of
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the last section.

src/estimator/kalman.jl

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superscript in e.g. ``\mathbf{X̂}_{k-1}^j(k)`` refers the vector at the ``j``th column of
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``\mathbf{X̂}_{k-1}(k)``. The symbol ``\mathbf{0}`` is a vector with zeros. The number of
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sigma points is ``n_σ = 2 n_\mathbf{x̂} + 1``. The matrices ``\sqrt{\mathbf{P̂}_{k-1}(k)}``
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and ``\sqrt{\mathbf{P̂}_{k}(k)}`` are the the lower triangular factors of [`cholesky`](https://docs.julialang.org/en/v1/stdlib/LinearAlgebra/#LinearAlgebra.cholesky)
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and ``\sqrt{\mathbf{P̂}_{k}(k)}`` are the the lower triangular factors of [`cholesky`](@extref Julia LinearAlgebra.cholesky)
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results. The correction and prediction step equations are provided below. The correction
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step is skipped if `estim.direct == true` since it's already done by the user.
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src/estimator/mhe/construct.jl

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- These functions are used inside the nonlinear optimization, so they must be type-stable
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and as efficient as possible.
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- The `JuMP` NLP syntax forces splatting for the decision variable, which implies use
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of `Vararg{T,N}` (see the [performance tip](https://docs.julialang.org/en/v1/manual/performance-tips/#Be-aware-of-when-Julia-avoids-specializing))
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of `Vararg{T,N}` (see the [performance tip](@extref Julia Be-aware-of-when-Julia-avoids-specializing))
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and memoization to avoid redundant computations. This is already complex, but it's even
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worse knowing that most automatic differentiation tools do not support splatting.
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- The signature of gradient and hessian functions is not the same for univariate (`nZ̃ == 1`)
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and multivariate (`nZ̃ > 1`) operators in `JuMP`. Both must be defined.
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Inspired from: [User-defined operators with vector outputs](https://jump.dev/JuMP.jl/stable/tutorials/nonlinear/tips_and_tricks/#User-defined-operators-with-vector-outputs)
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Inspired from: [User-defined operators with vector outputs](@extref JuMP User-defined-operators-with-vector-outputs)
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"""
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function get_optim_functions(
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estim::MovingHorizonEstimator,

src/estimator/mhe/execute.jl

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last time step ``k-1``. It then calls `JuMP.optimize!(estim.optim)` and extract the
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solution. A failed optimization prints an `@error` log in the REPL and returns the
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warm-start value. A failed optimization also prints [`getinfo`](@ref) results in
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the debug log [if activated](https://docs.julialang.org/en/v1/stdlib/Logging/#Example:-Enable-debug-level-messages).
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the debug log [if activated](@extref Julia Example:-Enable-debug-level-messages).
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"""
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function optim_objective!(estim::MovingHorizonEstimator{NT}) where NT<:Real
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model, optim = estim.model, estim.optim

src/sim_model.jl

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Sleep for `model.Ts` s minus the time elapsed since the last call to [`savetime!`](@ref).
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It calls [`sleep`](https://docs.julialang.org/en/v1/base/parallel/#Base.sleep) if `busywait`
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is `false`. Else, a simple `while` loop implements busy-waiting. As a rule-of-thumb,
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busy-waiting should be used if `model.Ts < 0.1` s, since the accuracy of `sleep` is around 1
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ms. Can be used to implement simple soft real-time simulations, see the example below.
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It calls [`sleep`](@extref Julia Base.sleep) if `busywait` is `false`. Else, a simple
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`while` loop implements busy-waiting. As a rule-of-thumb, busy-waiting should be used if
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`model.Ts < 0.1` s, since the accuracy of `sleep` is around 1 ms. Can be used to implement
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simple soft real-time simulations, see the example below.
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!!! warning
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The allocations in Julia are garbage-collected (GC) automatically. This can affect the

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