Direct shooting

[PierreMartinon]

First prototype: basic version with fixed step integration between time steps (midpoint).

Notes:

• implementation shares a lot of common code with collocation, using a new parameter 'control_steps' that corresponds to the number of steps for the inner integration over each time step. With control_steps=1 this is actually the same as collocation. Tests on the truck problem confirm this, with the same NLP dimensions and convergence (objective, iterations, time).
• currently, the OCP functions are evaluated using only the state values at the time steps, not the recomputed intermediate values. This leads to a lower accuracy of the discretized ODE, and for instance using 25 time steps and 10 control steps is less accurate than a collocation with 250 steps. This is mainly a choice of convenience, since the aim of the direct shooting is to use variable step ODE solvers anyway. This could be improved by recomputing the dynamics as needed, with the updated state values, instead of precomputing all dynamics at once.
• ADNLPModels only for now. For Examodels we may try the naive approach and loop over constraints components (the performance drop of this vs the current implementation in CTParser could be checked on the collocation discretizer)

Tasks

• add integral function to discretization API
• variables bounds
• objective function
• constraints function and bounds
• initial guess
• solution

[github-actions]

Breakage test results
Date: 2026-02-27 11:41:00

Name	Latest	Stable
OptimalControl	compat: v0.17.5-beta	compat: v1.0.2-beta