SI-OCP tightens safety tubes as control models adapt

Safety-critical controllers often convert uncertain model error into a fixed worst-case disturbance bound. That approach supports formal guarantees, but the resulting reachable sets and safety tubes can block feasible paths. Researchers at the University of Michigan propose Staggered Integral Online Conformal Prediction, or SI-OCP, which recalibrates the disturbance bound while the controller learns changing dynamics.

The SI-OCP paper was accepted to CDC 2026, and the authors released a GitHub repository. Their demonstration combines an online-adapted deep neural network with robust tube model predictive control, or MPC, on a quadcopter flying through spatially and temporally varying wind.

When calibration loses its labels

Conformal prediction uses a model’s previous errors to calibrate an interval or set for future predictions. Online conformal prediction adapts this process to sequential, potentially non-independent data and targets a user-specified long-run miss rate. That property suits controllers operating under drift, where model errors change during a mission.

Dynamics adaptation creates a labeling problem because conventional online conformal prediction expects the true error after each prediction. The natural label is the instantaneous residual between the system’s actual state derivative and the learned model’s estimate. A quadcopter typically measures quantities such as position, velocity, and attitude, while the required derivative-level residual remains unobserved.

MPC creates a separate coverage problem because it plans several steps ahead. A one-step error bound does not establish that the disturbance remains covered throughout the planning horizon, yet robust MPC needs a horizon-wide bound to construct a tube containing the possible trajectories around its nominal plan.