[AUD-007][High] Preserve reference tracking in precomputed MPC

[gabrielsantosphilips]

Audit finding

• ID: AUD-007
• Status: Verified defect
• Severity: High
• Confidence: High
• Audited revision: 2f479320d805a1f9f35ebe4afaaeeded48913a94

Problem

The precomputed MPC constructor accepts only H and F; referenceGainMatrix remains zero. SetReference() is still available and ComputeControl() uses that zero matrix.

Source:

numerical-toolbox-cpp/numerical/controllers/implementations/Mpc.hpp

Lines 108 to 116 in 2f47932

	template<typename T, std::size_t StateSize, std::size_t InputSize, std::size_t PredictionHorizon, std::size_t ControlHorizon>
	Mpc<T, StateSize, InputSize, PredictionHorizon, ControlHorizon>::Mpc(
	const HessianMatrix& precomputedH, const GradientMatrix& precomputedF,
	const MpcConstraints<T, InputSize>& constraints)
	: hessian(precomputedH)
	, gradientMatrix(precomputedF)
	, constraints(constraints)
	{}

and

numerical-toolbox-cpp/numerical/controllers/implementations/Mpc.hpp

Lines 228 to 239 in 2f47932

	typename Mpc<T, StateSize, InputSize, PredictionHorizon, ControlHorizon>::InputVector
	Mpc<T, StateSize, InputSize, PredictionHorizon, ControlHorizon>::ComputeControl(const StateVector& state)
	{
	auto g = gradientMatrix * state;
	if (reference)
	g = g - referenceGainMatrix * (*reference);
	auto negG = g * T(-1.0f);
	auto uOptimal = solvers::SolveSystem<T, TotalControlDim, 1>(hessian, negG);
	ApplyConstraints(uOptimal, negG);
	for (std::size_t k = 0; k < ControlHorizon; ++k)

Reproduction

At zero state with reference (3,0), an online MPC returned 16.6369629; a precomputed instance built from that MPC's H and F returned zero.

Acceptance criteria

• The precomputed API accepts all matrices required for supported reference tracking, or reference tracking is explicitly unavailable.
• Online and precomputed controllers produce matching control for nonzero state and reference.
• Add a parity TEST_F combining the precomputed constructor with SetReference().

[gabrielfrasantos]

Fixed and merged in #325 (d71b05f on main).

Reproduced first: with a nonzero reference and state, an online MPC returned 1.75439 while a precomputed instance built from its H and F returned -0.

The precomputed API now has a constructor taking the reference gain matrix alongside H and F, so a precomputed controller can track a reference. The existing three-argument constructor cannot support tracking, and that is now explicit rather than silent: SetReference asserts on an instance built that way instead of quietly using a zero gain matrix.

Test added: precomputed_controller_matches_online_reference_tracking builds the precomputed controller from the online one's GetHessian(), GetGradientMatrix() and GetReferenceGainMatrix(), sets the same reference, and asserts both produce the same nonzero control.

---

Generated by Claude Code