Robust MPC

Robust model predictive control (robust MPC) is a variant of model predictive control that guarantees constraint satisfaction and stability despite model uncertainty. Rather than optimizing for a single nominal model, robust MPC optimizes over a set of possible models — an uncertainty set — and computes a policy that satisfies constraints for all models in that set. The result is conservative: the controller hedges against the worst-case scenario within the uncertainty bounds, often at significant cost to nominal performance.

The mathematical machinery depends on how uncertainty is represented. Robust control theory provides several frameworks: tube-based MPC, where the state trajectory is constrained to stay within a tube around the nominal trajectory; min-max MPC, where the optimization explicitly minimizes over control inputs while maximizing over disturbance realizations; and scenario-based MPC, where the uncertainty set is sampled and the controller optimizes over the ensemble.

The trade-off between robustness and performance is the defining tension of the field. A robust MPC controller that is too conservative may never exploit favorable conditions; one that is too aggressive may fail precisely when the system deviates from the nominal model. The choice of uncertainty set is itself a design decision with no universal answer — it encodes the designer's risk tolerance and their beliefs about what kinds of deviation are plausible.

In safety-critical systems — autonomous vehicles, medical devices, power grids — robust MPC is often mandatory. The cost of a single constraint violation exceeds the accumulated cost of years of conservative operation. The implication is that robustness is not a technical add-on but a moral commitment: the willingness to accept suboptimal performance in exchange for guaranteed safety.