The Stochastic Robustness of Nominal and Stochastic Model Predictive Control

• 成果类型: Article
• 署名作者: Mcallister, Robert D.; Rawlings, James B.
• 署名单位: University of California System; University of California Santa Barbara
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3226712
• 发表日期: 2023
• 页码: 5810-5822
• 关键词: Model predictive control (MPC); stability of nonlinear systems; Stochastic systems; stochastic optimal control

摘要

In this work, we establish and compare the stochastic and deterministic robustness properties achieved by nominal model predictive control (MPC), stochastic MPC (SMPC), and a proposed constraint tightened MPC (CMPC) formulation, which represents an idealized version of tube-based MPC. We consider three definitions of robustness for nonlinear systems and bounded disturbances: robustly asymptotically stable (RAS), robustly asymptotically stable in expectation (RASiE), and RASiE with respect to the stage cost l() used in these MPC formulations (l-RASiE). Via input-to-state stability (ISS) and stochastic ISS (SISS) Lyapunov functions, we establish that MPC, subject to sufficiently small disturbances, and CMPC ensure all three definitions of robustness without a stochastic objective function. While SMPC is RASiE and l-RASiE, SMPC is not neccesarily RAS for nonlinear systems. Through a few simple examples, we illustrate the implications of these results and demonstrate that, depending on the definition of robustness considered, SMPC is not necessarily more robust than nominal MPC even if the disturbance model is exact.