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Leveraging Input Convex Neural Networks (ICNNs), ICNN-based Model PredictiveControl (MPC) successfully attains globally optimal solutions by upholdingconvexity within the MPC framework. However, current ICNN architecturesencounter the issue of vanishing/exploding gradients, which limits theirability to serve as deep neural networks for complex tasks. Additionally, thecurrent neural network-based MPC, including conventional neural network-basedMPC and ICNN-based MPC, faces slower convergence speed when compared to MPCbased on first-principles models. In this study, we leverage the principles ofICNNs to propose a novel Input Convex LSTM for Lyapunov-based MPC, with thespecific goal of reducing convergence time and mitigating thevanishing/exploding gradient problem while ensuring closed-loop stability. Froma simulation study of a nonlinear chemical reactor, we observed a mitigation ofvanishing/exploding gradient problem and a reduction in convergence time, witha percentage decrease of 46.7%, 31.3%, and 20.2% compared to baseline plainRNN, plain LSTM, and Input Convex Recurrent Neural Networks, respectively.

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