Horizon-Dependent Tube MPC for Spacecraft Rendezvous on Elliptical Orbits with Conditional Robust Constraint Satisfaction

What the math gives to ML

The paper offers a constructive robust-control mechanism with strong transfer potential: propagate an element-wise error tube over the prediction horizon using the actual time-varying closed-loop matrices, rather than a conservative constant-width tube. The recursion converts multiplicative parameter uncertainty and additive disturbances into a common bound and gives a computable Perron–Frobenius spectral-radius certificate for bounded tightening and an explicit input-to-state-stability gain. In neural networks, the same machinery can certify recurrent or state-space rollouts under activation, parameter, quantization, or model-prediction errors, and can tighten output constraints only at horizons where uncertainty has actually accumulated. The most useful experiments should measure the predicted spectral stability boundary and the saturation or divergence law of the propagated tube, not merely benchmark accuracy.