MCIS Safety Shield for Neural Controllers

Integrate this as a safety layer between the actor network and the environment in a low-dimensional model-based reinforcement-learning or neural-control benchmark. First discretize the state domain into axis-aligned boxes [x]. For each box, propagate interval bounds through the nominal plant plus neural residual network using interval arithmetic; for ReLU layers, use exact linear bounds when a neuron is sign-stable and lower and upper relaxations otherwise. Represent the current safe set S as a Boolean mask over boxes. Run predecessor iteration: initialize S=X_safe, enumerate candidate controls u from a grid or from the finite representative set, retain a state box [x] if at least one candidate satisfies F([x],u) subseteq S, and repeat until the mask stabilizes or reaches a fixed iteration budget. Pseudocode is: S=X_safe; repeat S_new={xbox in S: exists u in U_rep with F(xbox,u) subset S}; S=S_new until unchanged. At runtime, evaluate the actor action u_pi, test its interval image, and use u_pi if certified; otherwise choose the accepted candidate minimizing ||u-u_pi||^2. The interval bounds and fixed-point logic come from the mathematics; grid resolution, residual uncertainty bounds, and the action candidate set are engineering choices. Start with a 2D point-mass or cart-pole, comparing an unconstrained MLP actor, clipped-action shielding, and this MCIS shield. Measure constraint violations, episodic return, fraction of actor actions accepted, and conservatism as grid resolution changes. Success means zero simulated violations under bounded model error with substantially higher return than naive action clipping.