Input Convex LSTM: A Convex Approach for Fast Lyapunov-Based Model Predictive Control

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/exploding 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/exploding gradient problem while ensuring closed-loop stability. From a simulation study of a nonlinear chemical reactor, we observed a mitigation of vanishing/exploding 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 Networks, respectively.