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 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.