Explicit-MPC Safety Shield for Neural Policies

Integrate this as an inference-time wrapper around a continuous-control MLP, actor network, or RL policy. First solve robust finite-horizon QPs offline with a multiparametric-QP solver, retaining every polyhedral region $H_i x\le h_i$, affine action coefficient pair $(K_i,g_i)$, terminal or invariant-set certificate, and disturbance support value $d_j=\max_{w\in\mathcal W}F_{x,j}w$. Build a region lookup structure using a decision tree, active-set hash, or vectorized half-space tests. At runtime, compute $u_\theta=\pi_\theta(x)$, identify the region containing $x$, and evaluate input bounds, robust next-state inequalities, and the Lyapunov decrease margin. If any condition fails, return $u=K_i x+g_i$; alternatively find the smallest $\lambda\in[0,1]$ such that $u=(1-\lambda)u_\theta+\lambda u_i$ is certified. Pseudocode: i=find_region(x); u_nn=pi(x); if not safe(x,u_nn): u=K[i]@x+g[i]; else: u=u_nn. The paper supplies the explicit regions, affine laws, disturbance set, and reachability certificate; neural action statistics and fallback frequency are measured empirically. First test on a 2D double integrator with an MLP actor, bounded uniform disturbances, and robust MPC teacher, sweeping disturbance radius $\gamma$ and policy gain. The predicted signature is a sharp safety boundary: violations remain zero below the certified disturbance bound, while the unshielded policy violates constraints earlier. The shielded loop should enter the terminal set by the precomputed horizon $N$, within numerical tolerance, and fallback frequency should increase when the policy leaves certified regions.