Nonlinear Stochastic Model Predictive Control: Existence, Measurability, and Stochastic Asymptotic Stability

• 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.2022.3157131
• 发表日期: 2023
• 页码: 1524-1536
• 关键词: STOCHASTIC PROCESSES; asymptotic stability; stability analysis; COSTS; Closed loop systems; Predictive control; Robustness; stability of nonlinear systems; Stochastic systems; stochastic model predictive control (SMPC); stochastic optimal control

摘要

In this article, we establish a collection of new theoretical properties for nonlinear stochastic model predictive control (SMPC). Based on the concept of stochastic input-to-state stability (SISS), we define robust asymptotic stability in expectation (RASiE) and establish that nonlinear SMPC renders the origin of the closed-loop system RASiE. Moreover, we establish several new foundational results that have not been addressed in previous research. Specifically, we verify that, under basic regularity assumptions, a solution to the SMPC optimization problem exists and the closed-loop trajectory is Borel measurable thereby guaranteeing that all relevant stochastic properties of the closed-loop system are indeed well-defined. We present a numerical example to demonstrate the nonintuitive behavior that can arise from nonlinear SMPC.