setInitialTrajectory mutates the problem's initial state instead of validating the warm start

[astomodynamics]

Summary

CDDP::setInitialTrajectory() silently overwrites initial_state_ with X[0] from the provided trajectory.

Why this is a bug

A warm-start trajectory should seed the solver state, not change the optimization problem definition. With the current behavior, passing a mismatched X[0] changes the problem being solved instead of rejecting or repairing the input.

Code paths

• src/cddp_core/cddp_core.cpp:126-140
• src/cddp_core/cddp_core.cpp:272-305

setInitialTrajectory() assigns:

X_ = X;
U_ = U;
if (!X_.empty()) {
  initial_state_ = X_[0];
}

Later, initialization forces:

X_[0] = initial_state_;

So a caller-provided warm start can silently replace the original initial condition.

Expected behavior

One of these should happen instead:

• reject trajectories whose first state does not match initial_state_ within a tolerance, or
• keep initial_state_ authoritative and only use the rest of the trajectory as a warm start.

Impact

This can make solver results incorrect while looking superficially valid, because the library solves a different problem than the caller configured.

Suggested fix

• Stop mutating initial_state_ in setInitialTrajectory().
• Add validation for X[0] against the configured initial state.
• Add a regression test that passes a mismatched X[0] and verifies the solver either throws or preserves the original initial condition.