Near-Optimal Performance of Stochastic Model Predictive Control

• 成果类型: Article; Early Access
• 署名作者: Shin, Sungho; Na, Sen; Anitescu, Mihai
• 署名单位: Massachusetts Institute of Technology (MIT); University System of Georgia; Georgia Institute of Technology; United States Department of Energy (DOE); Argonne National Laboratory; University of Chicago
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.2023.0159
• 发表日期: 2026-01-28
• 关键词: stochastic optimal control; model predictive control; Stochastic Programming; performance analysis; Regret Analysis; receding horizon control; exponential decay; STABILITY; optimization; systems; DECOMPOSITION; sensitivity; state

摘要

This article presents a regret analysis for stochastic model predictive control (SMPC) in linear systems with quadratic performance index and additive and multiplicative uncertainties. Under a finite support assumption, the problem can be cast as a finitedimensional quadratic program, but the problem becomes quickly intractable as the problem size grows exponentially in the horizon length. SMPC aims to compute approximate solutions by solving a sequence of problems with truncated prediction horizons and committing the solution in a receding-horizon fashion. Although this approach is widely used in practice, its performance relative to the optimal solution is not well understood. This article reports for the first time a rigorous near-optimal performance guarantee of SMPC: under stabilizability and detectability conditions, the regret of SMPC is exponentially small in the prediction horizon length, allowing SMPC to achieve near-optimal performance at a substantially reduced computational expense.