[Roadmap] Update CTBenchmarks for OptimalControl v2 and benchmarking paper

[ocots]

Objective

Update CTBenchmarks.jl to be compatible with OptimalControl v2 and prepare a comprehensive benchmarking paper.

Context

CTBenchmarks.jl needs to be updated to work with the new OptimalControl v2 API. This includes updating problem formulations, solver interfaces, and benchmark infrastructure.

Why

Benchmarking is essential to validate the ecosystem and compare performance against other tools. A comprehensive benchmarking paper will showcase the capabilities of the control-toolbox ecosystem and provide reference performance data.

Scope

• Update for OptimalControl v2 compatibility
• Benchmark NLP solvers, modelers, linear solvers, AD backends
• Compare against CasADi, InfinitOpt, JuMP, Grape
• Write a comprehensive benchmarking article

References

• CTBenchmarks.jl
• Roadmap comment