jlesc

Author: jbcaillau

docs/make.jl

@@ -58,6 +58,7 @@ makedocs(;
             ],
         ],
         "Zhejiang 2025" => "zhejiang-2025.md",
+        "JLESC17" => "jlesc17.md",
     ],
 )
 

docs/src/jlesc17.md

@@ -0,0 +1,107 @@
+```@raw html
+<img width="800" alt="jlesc17" src="./assets/jlesc17.jpg">
+```
+
+# Solving optimal control problems on GPU with Julia
+
+### [Jean-Baptiste Caillau](http://caillau.perso.math.cnrs.fr), [Olivier Cots](https://ocots.github.io), [Joseph Gergaud](https://github.com/joseph-gergaud), [Pierre Martinon](https://github.com/PierreMartinon), [Sophia Sed](https://sed-sam-blog.gitlabpages.inria.fr)
+
+```@raw html
+<img width="800" alt="affiliations" src="./assets/affil.jpg">
+```
+
+## What it's about
+
+- Nonlinear optimal control of ODEs:
+
+$$ g(x(t_0),x(t_f)) + \int_{t_0}^{t_f} f^0(x(t), u(t))\, \mathrm{d}t \to \min $$
+
+subject to
+
+$$ \dot{x}(t) = f(x(t), u(t)),\quad t \in [t_0, t_f] $$
+
+plus boundary, control and state constraints
+
+- Our core interests: numerical & geometrical methods in control, applications
+- Why Julia: fast (+ JIT), strongly typed, high-level (AD, macros), available fast optimisation and ODE solvers, rapidly growing community
+
+```@raw html
+<img width="800" alt="juliacon2025" src="./assets/juliacon2025.jpg">
+```
+
+## Discretise then solve strategy (*aka* direct methods)
+
+- Discretising an OCP into an NLP: $h_i := t_{i+1}-t_i$,
+
+$$ g(X_0,X_N) + \sum_{i=0}^{N} h_i f^0(X_i,U_i) \to \min $$
+
+subject to 
+
+$$ X_{i+1} - X_i - h_i f(X_i, U_i) = 0,\quad i = 0,\dots,N-1 $$
+
+plus other constraints on $X := (X_i)_{i=0,N}$ and $U := (U_i)_{i=0,N}$ such as boundary and path (state and / or control) constraints :
+
+$$ b(t_0, X_0, t_N, X_N) = 0 $$
+
+$$ g(t_i, X_i, U_i) = 0,\quad i = 0,\dots,N $$
+
+- SIMD parallelism ($f0$, $f$, $g$) + sparsity: Kernels for GPU ([KernelAbstraction.jl](XXXX)) and sparse linear algebra ([CUDSS.jl](https://github.com/exanauts/CUDSS.jl))
+- Modelling and optimising for GPU: [ExaModels.jl](https://exanauts.github.io/ExaModels.jl/dev/guide)  + [MadNLP.jl](https://madnlp.github.io/MadNLP.jl), with **built-in AD**
+- [Simple example, DSL](@ref tutorial-double-integrator-energy)
+- Compile into an ExaModel (one pass compiler, [syntax + semantics](XXXX))
+- Simple example, generated code
+```julia
+```
+- **Remark.** Automated scalarisation of (linear) range constraints
+```julia
+```
+- Solving (MadNLP + CUDSS)
+```julia
+```
+- [Goddard problem](https://control-toolbox.org/Tutorials.jl/stable/tutorial-goddard/)
+```julia
+```
+
+## Wrap up
+
+- High level modelling of optimal control problems
+- Solving on CPU and GPU
+
+## Future
+
+- New [applications](XXXX) (space mechanics, biology, quantum mechanics and more)
+- Additional solvers: benchmarking on CPU / GPU for optimisation, Hamiltonian shooting and pathfollowing
+- Improved AD: collab between Argonne and Inria, [JLESC Shared Infra AD](https://jlesc.github.io/projects/shared_infra_ad) project (XXXX team)...
+- ... and open to contributions! If you like the package, please give us a star ⭐️
+
+```@raw html
+<a href="https://github.com/control-toolbox/OptimalControl.jl"><img width="800" alt="OptimalControl.jl" src="./assets/star.jpg"></a>
+```
+
+## control-toolbox.org
+
+- Open toolbox
+- Collection of Julia Packages rooted at [OptimalControl.jl](https://control-toolbox.org/OptimalControl.jl)
+
+```@raw html
+<a href="https://control-toolbox.org"><img width="800" alt="control-toolbox.org" src="./assets/control-toolbox.jpg"></a>
+```
+
+## Credits (not exhaustive!)
+
+- [ADNLPModels.jl](https://jso.dev/ADNLPModels.jl)
+- [DifferentiationInterface.jl](https://juliadiff.org/DifferentiationInterface.jl/DifferentiationInterface)
+- [DifferentialEquations.jl](https://docs.sciml.ai/DiffEqDocs)
+- [ExaModels.jl](https://exanauts.github.io/ExaModels.jl/dev/guide)
+- [Ipopt.jl](https://github.com/jump-dev/Ipopt.jl)
+- [MadNLP.jl](https://madnlp.github.io/MadNLP.jl)
+- [MLStyle.jl](https://thautwarm.github.io/MLStyle.jl)
+
+## Acknowledgements
+
+Jean-Baptiste Caillau is partially funded by a **France 2030** support managed by the *Agence Nationale de la Recherche*, under the reference ANR-23-PEIA-0004 ([PDE-AI](https://pde-ai.math.cnrs.fr) project).
+
+```@raw html
+<img width="150" alt="affiliations" src="./assets/france-2030.png">
+```
+