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For example as described by Garces, Strategies for Feedback Linearisation https://doi.org/10.1007/978-1-4471-0065-2.

sys, model: it's confusing

OptimizeResult like object
with additional attributes:

• estimated parameters
• covariance (see experiments)
• nrmse error (would require another jit / solve :-/ )
• Fit quantities here: https://se.mathworks.com/help/ident/ref/nlgreyest.html

see Berber, Ridvan, and Costas Kravaris, eds. Nonlinear Model Based Process Control. Dordrecht: Springer Netherlands, 1998. https://doi.org/10.1007/978-94-011-5094-1, pp. 246

Sources:

• https://ieeexplore.ieee.org/document/1231263/citations#citations
• leeLinearizationNonlinearControl2022, example 7.4.3

• https://www.sciencedirect.com/science/article/pii/S1474667017468406
• https://ieeexplore.ieee.org/abstract/document/9029804
• https://ieeexplore.ieee.org/abstract/document/4749432

Python bindings: https://cyipopt.readthedocs.io/en/latest/

Seems like the only places where they are used are in linearized.py. Here, one could just replace the default x0 values with required arguments of the right size.

This makes it more difficult to subclass.

Options:

1. ability to include initial state as part of the evolution instance. What about the case, when the initial state is only partially known?
2. fit_least_squares accepts an additional list with flags defining if state is estimated or given

Options:

1. Make user handle this by creating a new module with static fields.
2. Have a function that automatically creates a class with some given fields as static.
3. use eqx.filter. https://docs.kidger.site/equinox/api/filtering/partition-combine/

which = lambda tree: (tree.layers[-1].weight, tree.layers[-1].bias)
def fix_parameter(pytree, which):
    those = which(pytree)
    filter_spec = jtu.tree_map(lambda _: False, pytree)
    filter_spec = eqx.tree_at(
        which,
        filter_spec,
        replace=[True]*len(those),
    )