Recursive feasibility of conformal-prediction-based receding-horizon control

Ascertain general conditions and constructive methods that guarantee recursive feasibility of the receding-horizon optimization problems (equations (4.2) and (4.2_)) for closed-loop control with statistical abstractions, despite the constraint sets depending on a priori unknown environment predictions that are updated online. Provide a full solution ensuring that feasibility at the initial time implies feasibility at all subsequent times.

Background

The paper designs receding-horizon controllers that enforce safety using statistical abstractions of dynamic environments obtained via conformal prediction. The optimization problems (4.2) and (4.2_) include robust constraints that depend on predicted environment states $\hat{e}_{\tau|t}$, which change online.

Standard MPC approaches use terminal constraints/costs to ensure recursive feasibility, but here the constraint sets depend on predictions and are thus non-stationary, making classic guarantees inapplicable. The authors note shrinking-horizon schemes can enforce feasibility but a full, general solution remains unknown.