- Make control display conditional based on u_dim > 0
- Skip control in objective function display when u_dim == 0
- Skip control in dynamics arguments when u_dim == 0
- Skip control in 'where' clause when u_dim == 0
- Add test for display without control
- All tests pass (25/25 for control_zero, 4/4 for print regression)

This allows proper display of optimal control problems without control input.

- Add zero dimension handling in initial_control for Real input
- Add zero dimension handling in initial_control for Vector input
- Return empty vector function when control dimension is 0 and input is nothing
- Throw appropriate errors when trying to initialize zero-dim control with non-empty data
- Add comprehensive tests for initialization without control
- All tests pass (33/33 for control_zero, 239/239 for initial_guess regression)

This allows proper initialization of optimal control problems without control input.

Phase 6: Validation - No changes needed
- Name validation helpers already handle EmptyControlModel correctly via __is_control_set()
- Tests pass (39/39)

Phase 7: Serialization - No changes needed
- Serialization handles zero control dimension correctly (creates n×0 matrices)
- Tests pass (1831/1831)

Phase 8: Plotting - Skip control plots when dim=0
- Modified do_plot() in ext/plot_utils.jl to check control_dimension(sol) > 0
- Control plots are now skipped when control dimension is zero
- Tests pass (33/33)

All 8 phases of the refactoring are now complete. The codebase fully supports
optimal control problems without control input (control dimension = 0) while
maintaining backward compatibility.

Phase 6: Name validation tests
- Verify that control names are not collected when control is not set
- Test that 'u' can be used as state component name when control is empty

Phase 7: Serialization tests
- Test solution building with zero control dimension
- Verify control function returns empty vector
- Test solution properties (state_dimension, objective)

Phase 8: Plotting tests
- Import Plots at module level
- Test subplot count with :group layout (state + costate = 2 subplots)
- Test subplot count with :split layout (2 state + 2 costate = 4 subplots)
- Verify control plots are correctly skipped when dim=0

All tests pass (45/45) including the new comprehensive tests for
zero control dimension support.

…pport

Tests added to test_control_zero.jl:
- Serialization round-trip JSON export/import with control_dimension=0
- Serialization round-trip JLD2 export/import with control_dimension=0
- initial_control with empty vector Float64[] accepted when dim=0
- Plotting: explicit :control in description silently skipped when dim=0
- Plotting: state-only description with :split layout
- build() with variable but no control (dimension 0)
- Display: model without control but with variable (J(x,v) not J(x,u,v))

Docstrings updated:
- __is_control_set(::Model): clarify EmptyControlModel case
- PreModel: update control field type annotation
- dynamics!(ocp, f): remove outdated control precondition mention
- dynamics!(ocp, rg, f): same
- objective!(ocp, ...): remove control from preconditions list
- constraint!(ocp, ...): document control only needed for :control type
- build(pre_ocp): document control as optional, add zero-control example
- __print_mathematical_definition: document u_dim=0 behavior
- do_plot: document control skipped when control_dimension=0
- EmptyControlModel: enhance with usage context and See also refs