Heuristic Automatic Scenario Elimination in Stochastic Model Predictive Control

The performance of Model Predictive Control (MPC) degrades in the presence of uncertainties such as measurement noise, model inaccuracies, and external disturbances. To deal with this issue, stochastic MPC incorporates uncertainty into predictions, either explicitly via probability density functions or implicitly via scenarios, optimizing control actions with probabilistic constraint satisfaction guarantees. However, scenario-based approaches rely on careful scenario selection to avoid a conservative control law. To mitigate this issue, this paper uses slack variables to manage constraint violations and relieve conservatism, allowing the controller to occasionally violate constraints according to a tuning parameter that balances the trade-off between performance and risk.