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

2025-12-11

AI Summary

This paper addresses stochastic model predictive control (MPC) for linear systems under unknown disturbance distributions, subject to joint time-point chance constraints. We propose a distribution-free, computationally efficient output-feedback framework. Our method leverages conformal prediction—applied for the first time to construct finite-sample confidence sets for error trajectories—without distributional assumptions, parametric modeling, or offline re-optimization. Integrating probabilistic set-based MPC with an indirect feedback mechanism ensures recursive feasibility and rigorous closed-loop chance constraint satisfaction. Theoretically, we prove constraint satisfaction and recursive feasibility. Numerical experiments demonstrate that, compared to state-of-the-art approaches, our framework significantly reduces conservatism—achieving an average 23% reduction in constraint relaxation—and improves online computational efficiency, solving each MPC instance 3.1× faster.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

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.

Problem

• Develops stochastic MPC for linear systems with joint-in-time chance constraints under unknown disturbance distributions.
• Uses conformal prediction to create finite-sample confidence regions for stochastic error trajectories efficiently.
• Extends the approach to output feedback settings with unknown measurement noise distributions.

Innovation

• Uses conformal prediction for confidence regions
• Employs indirect feedback for feasibility guarantees
• Extends to output feedback with unknown noise