Nonlinear Stochastic Model Predictive Control: Existence, Measurability, and Stochastic Asymptotic Stability
Nonlinear Stochastic Model Predictive Control: Existence, Measurability, and Stochastic Asymptotic Stability
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DOI：
10.1109/tac.2022.3157131
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发表时间：
2023-03
影响因子：
6.8
通讯作者：
Robert D. McAllister;J. Rawlings
中科院分区：
文献类型：
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作者：
Robert D. McAllister;J. Rawlings
在本文中，我们为非线性随机模型预测控制（SMPC）建立了新的理论特性集合。基于随机输入到国家稳定性（SISS）的概念，我们定义了预期的稳健渐近稳定性（RASIE），并确定非线性SMPC呈现出闭环系统Rasie的起源。此外，我们建立了几个新的基础结果，这些结果尚未解决。具体而言，我们验证，在基本的规则性假设下，存在SMPC优化问题的解决方案，并且闭环轨迹是可测量的，从而确保闭环系统的所有相关随机特性确实是明确定义的。我们提出了一个数值示例，以证明非线性SMPC可能产生的非直觉行为。
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.