MPC "constrained" solve is post-hoc clipping, not a constrained QP

[gabrielfrasantos]

Severity: high
Domain: controllers
Status: VERIFIED — read + hand-traced against a210d34 on 2026-08-10
Suggested labels: bug, numerical-correctness, controllers

Summary

Mpc::ComputeControl() solves the unconstrained system and then clamps each control element
independently. For a coupled Hessian this does not produce the constrained optimum. There are also
no state or output constraints, despite the documentation presenting constrained MPC.

Location

numerical/controllers/implementations/Mpc.hpp

Evidence

auto uOptimal = solvers::SolveSystem<T, TotalControlDim, 1>(hessian, negG);
ApplyConstraints(uOptimal);

for (std::size_t k = 0; k < ControlHorizon; ++k)
    for (std::size_t i = 0; i < InputSize; ++i)
    {
        auto& val = u.at(k * InputSize + i, 0);
        val = std::max(std::min(val, constraints.uMax->at(i, 0)), constraints.uMin->at(i, 0));
    }

Each element is clamped in isolation; no active-set re-optimisation occurs.

Trace

H = [[2,1],[1,2]], g = [−4,−2], constraint u₁ ≤ 1:

unconstrained optimum:  H⁻¹(−g) = [2, 0]
clipped:                [1, 0]
true constrained optimum (active set u₁ = 1):
    minimise over u₂ with u₁ fixed at 1  =>  2u₂ + 1 = 2  =>  u₂ = 0.5
                            [1, 0.5]

Clipping loses the compensation that the remaining free variables should provide.

Why tests do not catch it

The MPC test asserts only that the result lies within [uMin, uMax]. A clipped, non-optimal
sequence satisfies that.

Suggested fix

Implement a bounded active-set box-QP solver (no heap, fixed iteration cap) and use it in place
of SolveSystem + clamp. Add a test comparing against an analytically known constrained optimum
such as the one above.

SolveSystem is also called without a status check — see issue 004.

Notes

Depends on the "Priority 0" box-QP recommendation in the audit report. Related: issue 010 (reference
tracking).