Leveraging Input Convex Neural Networks (ICNNs), ICNN-based Model Predictive
Control (MPC) successfully attains globally optimal solutions by upholding
convexity within the MPC framework. However, current ICNN architectures
encounter the issue of vanishing gradients, which limits their ability to serve
as deep neural networks for complex tasks. Additionally, the current neural
network-based MPC, including conventional neural network-based MPC and
ICNN-based MPC, faces slower convergence speed when compared to MPC based on
first-principles models. In this study, we leverage the principles of ICNNs to
propose a novel Input Convex LSTM for Lyapunov-based MPC, with the specific
goal of reducing convergence time and mitigating the vanishing gradient problem
while ensuring closed-loop stability. From a simulation study of a nonlinear
chemical reactor, we observed a mitigation of vanishing gradient problem and a
reduction in convergence time, with a percentage decrease of 46.7%, 31.3%, and
20.2% compared to baseline plain RNN, plain LSTM, and Input Convex Recurrent
Neural Network, respectively.

该研究基于输入凸神经网络（ICNN），提出了一种用于基于 Lyapunov 的 MPC 的新型输入凸 LSTM，旨在减少收敛时间、缓解梯度消失问题并确保闭环稳定性。模拟非线性化学反应器实验结果显示，相对于基准普通循环神经网络、普通 LSTM 和输入凸循环神经网络，梯度消失问题减轻并且收敛时间分别降低了 46.7%、31.3% 和 20.2%。