This article analyzes the stability-related properties of long short-term memory (LSTM) networks and investigates their use as the model of the plant in the design of model predictive controllers (MPC). First, sufficient conditions guaranteeing the Input-to-State stability (ISS) and Incremental Input-to-State stability (ISS) of LSTM are derived. These properties are then exploited to design an observer with guaranteed convergence of the state estimate to the true one. Such observer is then embedded in a MPC scheme solving the tracking problem. The resulting closed-loop scheme is proved to be asymptotically stable. The training algorithm and control scheme are tested numerically on the simulator of a pH reactor, and the reported results confirm the effectiveness of the proposed approach.

中文翻译：

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具有长短期记忆网络的学习模型预测控制

本文分析了长短期记忆 (LSTM) 网络的稳定性相关特性，并研究了它们在模型预测控制器 (MPC) 设计中用作工厂模型的用途。首先，推导出保证LSTM的输入到状态稳定性（ISS）和增量输入到状态稳定性（ISS）的充分条件。然后利用这些属性来设计一个观察者，保证状态估计收敛到真实状态。然后将这种观察器嵌入到解决跟踪问题的 MPC 方案中。由此产生的闭环方案被证明是渐近稳定的。训练算法和控制方案在pH反应器模拟器上进行了数值测试，报告的结果证实了所提出方法的有效性。