added: treat continuity constraints as linear in OrthogonnalCollocation#397
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They are detailed in the extended help, like for all the other transcription methods.
This is a bit more explicit. The matrix equation in `init_defectmat` is harder to follow.
franckgaga
changed the title
OrthogonnalCollocationOrthogonnalCollocation
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I just realized that the continuity constraints of the
OrthogonalCollocationtranscription are in fact linear equality constraints 😮😮😮 ! I'm not sure if I'm the first one to notice this, presumably not, but nobody mention this in all the textbooks, papers and online documentation that I read.This PR introduces the change to treat them as linear. The main gain from this change is reducing the size of the Jacobian and Hessian of the Langrangian for the AD of the nonlinear equality constraints. The performances gains at NLP solving itself is presumably negligible, except if the solver treat linear constraints separately.
Note that for
:gaussradau, the continuity constraint is useless and redundant. It is however simpler to keep this redundant constraint, since it keeps an identical logic for all quadrature schemes. Now that the continuity constraint is treated as linear and no longer included in the AD, entirely removing it would significantly complexify the internal logic, and presumably without much difference on the performances.In the end, the linear equality constraint include the continuity constraint and the defect of the stochastic states (for the linear unmeasured disturbance model i.e. the integrators). One exception: the state vector is not augmented with
InternalModel, so there are only the continuity constraints for this case.