Learning-enabled Acceleration of Scenario-based Model Predictive Control

2026-07-14

AI Summary

This work addresses the computational challenges of scenario-based model predictive control (SBMPC), whose complexity grows rapidly with the number of scenarios and prediction horizon, hindering real-time implementation. To overcome this limitation, the authors propose an efficient parallel solution framework that first reformulates SBMPC as a consensus optimization problem, enabling dual-level parallel decomposition across both scenarios and time steps via the alternating direction method of multipliers (ADMM). A key innovation is the novel incorporation of Moreau envelope learning to accelerate dual variable updates, complemented by explicit handling of nonanticipativity constraints. Evaluated on a microgrid energy management task, the proposed method significantly outperforms state-of-the-art solvers IPOPT and MadNLP, achieving order-of-magnitude speedups while maintaining high control accuracy, thereby demonstrating its practical viability for large-scale stochastic MPC applications.

Abstract

Scenario-based model predictive control (SBMPC) is a variant of model predictive control (MPC) that explicitly accounts for uncertainty by optimizing control actions over multiple predicted scenarios. However, its computational complexity increases rapidly with the number of scenarios and prediction horizon, limiting is applicability to real-time planning and control. This paper presents a learning-accelerated Alternating Direction Method of Multipliers (ADMM) algorithm for efficiently solving SBMPC problems by leveraging parallel computing and Moreau envelope learning, while maintaining high solution accuracy. We reformulate the SBMPC problems into consensus forms that can be decomposed via ADMM, separating the scenario-dependent dynamics from non-anticipativity constraints and enabling parallel updates across scenarios and time steps. Building on this decomposition, we utilize existing learning-to-optimize schemes, which leverages Moreau envelope learning of the cost function to accelerate the primal update in ADMM, thereby reducing computation time. The proposed framework is evaluated on a microgrid energy management problem subject to load and renewable generation uncertainties. Comparisons with IPOPT and MadNLP, popular and modern nonlinear programming solvers, demonstrate substantial computational speedups while maintaining reliable closed-loop control performance.

Problem

• Scenario-based Model Predictive Control
• computational complexity
• real-time control
• uncertainty

Innovation

• learning-accelerated ADMM
• scenario-based MPC
• Moreau envelope learning
• parallel decomposition
• non-anticipativity constraints