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Add a tutorial section covering the `initial_trajectory` keyword: the
map-from-states-to-functions form, that unlisted states keep their constant
`u0map` seed, backend support (JuMP, InfiniteOpt, CasADi), and the normalized
`[0, 1]` time base used for free final time problems.
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Each function is evaluated at the collocation points to produce the start values
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handed to the optimizer. Only the states listed are affected — the rest keep their
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constant seed. This changes where the solve starts from, not the optimum it
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converges to.
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`initial_trajectory` is supported by the JuMP, InfiniteOpt, and CasADi backends.
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Passing a non-empty map to Pyomo raises an `ArgumentError`.
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!!! note
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For free final time problems (see below) the collocation grid is normalized to
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`[0, 1]`, so the trajectory functions receive normalized time rather than
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physical time.
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### Free final time problems
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There are additionally a class of dynamic optimization problems where we would like to know how to control our system to achieve something in the least time. Such problems are called free final time problems, since the final time is unknown. To model these problems in ModelingToolkit, we declare the final time as a parameter.
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