Robust Condensing for LPV-MPC With Asymptotically Constant Complexity

• 成果类型: Article
• 署名作者: Cimini, Gionata; Bemporad, Alberto
• 署名单位: IMT School for Advanced Studies Lucca
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3635913
• 发表日期: 2026
• 关键词: model-predictive control; set; algorithms

摘要

This article presents a highly efficient method for robustly eliminating equality constraints in optimization problems arising from model predictive control (MPC). Such a condensing operation is often implemented to reduce the number of optimization variables through the direct elimination of state variables by substitution, a procedure which is prone to numerical instability and whose complexity scales linearly with the prediction horizon. We propose a novel blocked QR decomposition algorithm for condensing MPC problems in a numerically robust manner. The method is applicable when the system dynamics, described by either linear or linearized models, are time-invariant over the prediction horizon. The method effectively handles unstable dynamics and exhibits numerical convergence properties that result in an asymptotically constant computational complexity regardless of the horizon length. We benchmark our method against state-of-the-art algorithms for robust condensing of dynamic optimization problems, demonstrating significantly superior results. For sufficiently long horizons, the proposed algorithm can even outperform direct state elimination in terms of speed.