feat: Add support for zero control dimension (NLP_u = 0)

[ocots]

• Add efficiency guards in DOCP_variables.jl and ode/common.jl
• Fix reshape bug in collocation.jl for zero control dimension
• Add parameter estimation test problems (estimate_initial_condition, estimate_rotation_rate, least_squares_with_constraint)
• Add comprehensive unit tests (49 tests) for zero control allocations
• Add integration tests (118 tests) for zero control dimension
• All tests pass successfully

[ocots]

Add support for zero control dimension (NLP_u = 0)

This PR implements full support for optimal control problems with zero control dimension in CTDirect.jl, enabling parameter estimation.

Problem Statement

Previously, CTDirect.jl did not properly handle problems where NLP_u = 0 (no control variables). This caused:

• Unnecessary loops over empty control arrays
• Allocation issues in initial guess construction
• Reshape errors in collocation methods
• Missing test coverage for this edge case

Solution

1. Efficiency Guards in Source Code

src/DOCP_variables.jl

Added guard to skip control bounds loops when NLP_u = 0:

if docp.dims.NLP_u > 0
    for i in 1:(docp.time.steps + 1)
        for j in 1:docp.time.control_steps
            set_control_at_time_step!(var_l, u_lb, docp, i; j=j)
            set_control_at_time_step!(var_u, u_ub, docp, i; j=j)
        end
    end
end

Similar guard added in __initial_guess to avoid iterating over control steps.

src/ode/common.jl

Added early return in control getter when dimension is zero:

function get_control_at_time_step(xu, docp::DOCP, time_step::Int)
    docp.dims.NLP_u == 0 && return view(xu, 1:0)  # Empty view
    # ... rest of implementation
end

src/collocation.jl

Fixed reshape bug for ExaModel initial guess when m = 0:

m = CTModels.control_dimension(ocp)
if m > 0
    control = hcat([x0[(n + 1 + i * (n + m)):(n + 1 + i * (n + m) + m - 1)] for i in 0:(N - 1)]...,)
    control = [control control[:, end]]
else
    control = zeros(0, N + 1)  # Empty control array
end

2. Parameter Estimation Test Problems

Created three well-posed parameter estimation problems in test/problems/autonomous_system.jl:

• estimate_initial_condition(): Estimate initial condition of harmonic oscillator to reach target final state
• estimate_rotation_rate(): Estimate rotation rate parameter in dynamics
• least_squares_with_constraint(): Least squares fit with path constraint

All problems use proper CTModels syntax:

• Mutating dynamics: dynamics!(r, t, x, u, v) = r .= ...
• Complete signatures with u and v parameters even when unused
• Proper definition! and time_dependence! calls

3. Comprehensive Test Coverage

Unit Tests (test/ci/test_zero_control_allocations.jl) - 49 tests

• DOCP creation and dimension verification
• Control getters return empty views
• Control setters are no-ops
• All schemes support zero control
• Variables bounds with zero control
• Initial guess construction
• Sparsity patterns

Integration Tests (test/ci/test_zero_control.jl) - 118 tests

• All discretization schemes (euler, midpoint, trapeze)
• Parameter estimation problems
• Solution dimensions verification
• Initial guess with empty control
• ADNLP manual backend

4. Test Suite Restoration

Restored full test suite in test/runtests.jl - all 167+ tests pass successfully.

Testing Results

✅ :param_estimation :all_schemes        6/6 tests passed
✅ :param_estimation :rotation_rate      3/3 tests passed  
✅ :param_estimation :with_constraint    2/2 tests passed
✅ :param_estimation :solution_dimensions 105/105 tests passed
✅ :zero_control_allocations            49/49 tests passed
✅ All CTDirect tests passed

Benefits

• ✅ Enables parameter estimation problems (Kaplan-style)
• ✅ Supports autonomous systems without control
• ✅ Improves performance by avoiding unnecessary iterations
• ✅ Prevents allocation bugs in edge cases
• ✅ Comprehensive test coverage for zero control dimension
• ✅ Maintains backward compatibility with existing code

Breaking Changes

None - this is a pure addition of functionality.

[ocots]

Implementation Notes

CTParser Limitation

Currently, CTParser does not support zero control dimension problems. Therefore, all test problems must be defined using CTModels.PreModel API instead of the @def macro syntax.

Why CTModels is required:

• CTParser assumes at least one control variable in its parsing logic
• The @def macro generates code that expects NLP_u > 0
• No control! call is possible for zero control dimension problems

Test Implementation:
All test problems in test/problems/autonomous_system.jl use:

pre = CTModels.PreModel()
CTModels.time!(pre; t0=0.0, tf=1.0)
CTModels.state!(pre, 2)
CTModels.variable!(pre, n)  # For parameter estimation
# ... dynamics, objective, constraints ...
CTModels.definition!(pre, quote ... end)
CTModels.time_dependence!(pre; autonomous=true/false)
ocp = CTModels.build(pre)

Future Work:
Enhancing CTParser to support zero control dimension would allow users to write:

@def begin
    t ∈ [0, 1], time
    x ∈ R², state
    v ∈ Rⁿ, variable  # parameters only, no control
    x(0) == v
    ẋ(t) == f(t, x, v)
    objective → min
end

For now, CTModels provides the necessary flexibility to define parameter estimation problems with zero control dimension.

[ocots]

@PierreMartinon please review and merge

ps: @jbcaillau waiting for a new beta release of CTParser

[github-actions]

Breakage test results
Date: 2026-03-25 15:30:09

Name	Latest	Stable
OptimalControl	compat: v1.0.5	compat: v1.0.5

[PierreMartinon]

Note: for now I have commented the inclusion of ode/variable.jl to remove the dependency on DifferentialEquations. This will be reintroduced when the difficulties with AD over variable step ODE are solved.