Updated broken links

docs/src/examples/echo_ren.md

@@ -5,7 +5,7 @@
 
 RENs and LBDNs can be used for a lot more than just learning-based problems. In this example, we'll see how RENs can be used to design nonlinear feedback controllers with stability guarantees for linear dynamical systems with constraints. Introducing constraints (eg: minimum/maximum control inputs) often means that nonlinear controllers perform better than linear policies. A common approach is to use *Model Predictive Control* ([MPC](https://en.wikipedia.org/wiki/Model_predictive_control)). In our case, we'll use convex optimisation to design a nonlinear controller. The controller will be an [*echo state network*](https://en.wikipedia.org/wiki/Echo_state_network) based on a contracting REN. We'll use this alongside the [*Youla-Kucera parameterisation*](https://www.sciencedirect.com/science/article/pii/S1367578820300249) to guarantee stability of the final controller.
 
-For a detailed explanation of the theory behind this example, please read Section IX of the original [paper](https://ieeexplore.ieee.org/document/10179161). For more on using RENs with the Youla parameterisation, see [Wang et al. (2022)](https://ieeexplore.ieee.org/abstract/document/9802667) and [Barbara, Wang & Manchester (2023)](https://doi.org/10.48550/arXiv.2304.06193).
+For a detailed explanation of the theory behind this example, please read Section IX of the original [paper](https://ieeexplore.ieee.org/document/10179161). For more on using RENs with the Youla parameterisation, see [Wang et al. (2022)](https://ieeexplore.ieee.org/abstract/document/9802667) and [Barbara, Wang & Manchester (2023)](https://arxiv.org/abs/2304.06193v2).
 
 
 ## 1. Background theory
@@ -59,7 +59,7 @@ It turns out that if we augment the original controller with ``\tilde{u} = \math
 z = \mathcal{T}_0 d + \mathcal{T}_1 \mathcal{Q}(\mathcal{T}_2 d)
 ```
 
-This is an old idea in linear control theory called the Youla-Kucera parameterisation. We extended it to nonlinear models (like RENs) and nonlinear dynamical systems in [Wang et al. (2022)](https://ieeexplore.ieee.org/abstract/document/9802667) and [Barbara, Wang & Manchester (2023)](https://doi.org/10.48550/arXiv.2304.06193), respectively.
+This is an old idea in linear control theory called the Youla-Kucera parameterisation. We extended it to nonlinear models (like RENs) and nonlinear dynamical systems in [Wang et al. (2022)](https://ieeexplore.ieee.org/abstract/document/9802667) and [Barbara, Wang & Manchester (2023)](https://arxiv.org/abs/2304.06193v2), respectively.
 
 
 ### Echo state networks with REN

docs/src/examples/rl.md

@@ -2,7 +2,7 @@
 
 *Full example code can be found [here](https://github.com/acfr/RobustNeuralNetworks.jl/blob/main/examples/src/lbdn_rl.jl).*
 
-One of the original motivations for developing `RobustNeuralNetworks.jl` was to guarantee stability and robustness in learning-based control. Some of our recent research (eg: [Wang et al. (2022)](https://ieeexplore.ieee.org/abstract/document/9802667) and [Barbara, Wang & Manchester (2023)](https://doi.org/10.48550/arXiv.2304.06193)) has shown that, with the right controller architecture, we can learn over a space of stabilising controllers for linear/nonlinear systems using standard reinforcement learning techniques, so long as our control policy is parameterised by a REN (see also [(Convex) Nonlinear Control with REN](@ref)).
+One of the original motivations for developing `RobustNeuralNetworks.jl` was to guarantee stability and robustness in learning-based control. Some of our recent research (eg: [Wang et al. (2022)](https://ieeexplore.ieee.org/abstract/document/9802667) and [Barbara, Wang & Manchester (2023)](https://arxiv.org/abs/2304.06193v2)) has shown that, with the right controller architecture, we can learn over a space of stabilising controllers for linear/nonlinear systems using standard reinforcement learning techniques, so long as our control policy is parameterised by a REN (see also [(Convex) Nonlinear Control with REN](@ref)).
 
 In this example, we'll demonstrate how to train an LBDN controller with *Reinforcement Learning* (RL) for a simple nonlinear dynamical system. This controller will not have any stability guarantees. The purpose of this example is simply to showcase the steps required to set up RL experiments for more complex systems with RENs and LBDNs.
 
@@ -108,7 +108,7 @@ cost(z::AbstractVector, qref, uref) = mean(_cost.(z, (qref,), (uref,)))
 
 ## 3. Define a model
 
-For this example, we'll learn an LBDN controller with a Lipschitz bound of ``\gamma = 20``. Its inputs are the state ``x_t`` and goal position ``q_\mathrm{ref}``, while its outputs are the control force ``u_t``. We have chosen a model with two hidden layers each of 32 neurons just as an example. For details on how Lipschitz bounds can be useful in learning robust controllers, please see [Barbara, Wang & Manchester (2023)](https://doi.org/10.48550/arXiv.2304.06193).
+For this example, we'll learn an LBDN controller with a Lipschitz bound of ``\gamma = 20``. Its inputs are the state ``x_t`` and goal position ``q_\mathrm{ref}``, while its outputs are the control force ``u_t``. We have chosen a model with two hidden layers each of 32 neurons just as an example. For details on how Lipschitz bounds can be useful in learning robust controllers, please see [Barbara, Wang & Manchester (2023)](https://arxiv.org/abs/2304.06193v2).
 
 ```julia
 using Flux

docs/src/index.md

@@ -63,4 +63,4 @@ The REN parameterisation was extended to continuous-time systems in [yet to be i
 
 See below for a collection of projects and papers using `RobustNeuralNetworks.jl`.
 
-> N. H. Barbara, R. Wang, and I. R. Manchester, "Learning Over Contracting and Lipschitz Closed-Loops for Partially-Observed Nonlinear Systems," April 2023. doi: [https://doi.org/10.48550/arXiv.2304.06193](https://doi.org/10.48550/arXiv.2304.06193).
+> N. H. Barbara, R. Wang, and I. R. Manchester, "Learning Over Contracting and Lipschitz Closed-Loops for Partially-Observed Nonlinear Systems," April 2023. doi: [https://arxiv.org/abs/2304.06193v2](https://arxiv.org/abs/2304.06193v2).