Distributionally robust two-stage model predictive control: adaptive constraint tightening with stability guarantee

A team of researchers has introduced a novel control algorithm, the Two-Stage Distributionally Robust Model Predictive Control (TSDR-MPC), designed to make autonomous systems like robots and drones safer and more efficient. The core challenge they address is the inherent uncertainty in real-world environments, where disturbances (like wind gusts or sensor noise) have unknown and shifting statistics. Traditional robust MPC is overly cautious, while stochastic MPC requires perfect knowledge of disturbance patterns, which is rarely available. The new TSDR-MPC framework bridges this gap by using Distributionally Robust Optimization (DRO) to handle a "worst-case" within a set of possible distributions, leading to less conservative and more adaptive control.

The key innovation is a two-stage optimization structure. The first stage handles the standard control cost, while the second stage explicitly formulates and penalizes potential constraint violations. This allows the system to adaptively tighten its safety margins based on observed disturbances, using a mathematically defined "Wasserstein ambiguity set" to model uncertainty. The researchers provide a tractable reformulation of the complex problem and a cutting-plane algorithm proven to converge quickly for real-time use. Crucially, they also designed a special terminal constraint applied only to the nominal system, which guarantees closed-loop stability even when disturbances have a non-zero average bias—a common real-world scenario where previous methods could fail. Numerical simulations validate that the framework maintains robustness across various disturbance scenarios where other methods would be either unsafe or too restrictive.