Finite-Candidate Neural Reference Shield

1. Integration point: attach the layer between an NN policy or trajectory head and the low-level controller. The network emits $z_t$, while measured state $x_t$ supplies speed, position, current, voltage, and other quantities needed to evaluate state-dependent constraints. Encode current and voltage limits such as $i_d^2+i_q^2\leq I_{\max}^2$ and $u_d^2+u_q^2\leq V_{\mathrm{dq,max}}^2$, together with the paper's kinematic limits, as $g_j(r,x)\leq0$. 2. Pseudocode: evaluate every constraint; enumerate active sets permitted by command dimension; for each active set solve the stationarity and active-boundary equations using the paper's closed-form expressions or small eigenvalue construction; discard candidates with violated inactive constraints or negative multipliers; return the feasible candidate with minimum weighted distance to $z_t$. If none passes tolerances, use a conservative interior fallback. Initially stop gradients through the shield, then test implicit differentiation. 3. Computed versus estimated: constraint values, candidates, feasibility, and objective are computed analytically; model mismatch, noise margins, and tolerances are estimated empirically. 4. First cheap experiment: use a 2D MLP policy controlling a simulated PMSM or constrained point-mass servo. Compare raw output, penalty training, iterative projected-gradient projection, and this shield. Sweep command magnitude and measure violations, latency, and tracking error. The prediction is a sharp feasibility transition: interior commands satisfy $r^*=z$ up to tolerance, while exterior commands have zero violations and increasing residual beginning at the boundary. The solver should agree with a high-accuracy nonlinear optimizer within $10^{-5}$ and have nearly constant runtime; measured transition locations should match the analytically computed feasible boundary within 5%.