Abstract This paper discusses the stability properties of a robust nonlinear model predictive control (NMPC) scheme that is based on a multi-stage optimization formulation. The use of a scenario tree to represent the uncertainty makes it possible to formulate a closed-loop robust approach with recourse which improves the open-loop approach in terms of performance and domain of attraction. We show that a straightforward formulation of a multi-stage NMPC scheme does not guarantee Input-to-State stability (ISS) in a deterministic setting, in contrast to the results that one gets using stochastic stability concepts. Since for many applications deterministic stability guarantees are desired, we provide an alternative formulation to achieve deterministic ISS and recursive feasibility guarantees for the case of discrete values of the uncertainty. The design and the performance of the proposed schemes are illustrated by simulations for a highly nonlinear example.

中文翻译：

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多级非线性模型预测控制的稳定性特性

摘要 本文讨论了基于多级优化公式的鲁棒非线性模型预测控制 (NMPC) 方案的稳定性特性。使用场景树来表示不确定性，可以制定具有追索权的闭环稳健方法，从而在性能和吸引力方面改进开环方法。我们表明，与使用随机稳定性概念获得的结果相比，多阶段 NMPC 方案的直接公式并不能保证确定性设置中的输入到状态稳定性 (ISS)。由于许多应用需要确定性稳定性保证，因此我们提供了一种替代公式，以在不确定性离散值的情况下实现确定性 ISS 和递归可行性保证。