Distribution-Free Stochastic MPC for Joint-in-Time Chance-Constrained Linear Systems

This work presents a stochastic model predictive control (MPC) framework for linear systems subject to joint-in-time chance constraints under unknown disturbance distributions. Unlike existing stochastic MPC formulations that rely on parametric or Gaussian assumptions or require expensive offline computations, the proposed method leverages conformal prediction (CP) as a streamlined tool to construct finite-sample confidence regions for the system's stochastic error trajectories with minimal computational effort. These regions enable the relaxation of probabilistic constraints while providing formal guarantees. By employing an indirect feedback mechanism and a probabilistic set-based formulation, we prove recursive feasibility of the relaxed optimization problem and establish chance constraint satisfaction in closed-loop. Furthermore, we extend the approach to the more general output feedback setting with unknown measurement noise distributions. Given available noise samples, we establish satisfaction of the joint chance constraints and recursive feasibility via output measurements alone. Numerical examples demonstrate the effectiveness and advantages of the proposed method compared to existing approaches.