Traditional Lyapunov-based model predictive control (LMPC) using machine learning models typically involves three sequential steps: developing a machine learning (ML) model, designing a Lyapunov function for stability guarantees, and constructing the model predictive controller (MPC). However, these steps are inherently interdependent, and improper design in one component, such as the ML model or the Lyapunov function, can adversely affect controller design and closed-loop performance. To overcome these challenges, we propose an end-to-end machine learning-based Lyapunov-stable MPC (E2E-MLMPC) framework that simultaneously learns the Lyapunov function and MPC policy for nonlinear systems directly from data. Given a pre-trained ML model, a stabilizing control policy is learned within a unified computational graph that integrates the ML-based dynamics, system constraints, and Lyapunov stability conditions. The neural policy parameters are optimized via automatic differentiation, enabling end-to-end training with explicit stability certification. A rigorous theoretical analysis is provided to establish the closed-loop stability of the resulting controller. Furthermore, since the learned controller is implemented as a neural network, it substantially reduces online computation time compared with traditional ML-based MPC schemes. Simulation studies demonstrate that the proposed E2E-MLMPC framework achieves stable and efficient control performance in a chemical reactor example. • End-to-end framework for developing machine learning-based predictive controller. • Learn neural control policy and neural Lyapunov function simultaneously. • Rigorous stability proof and fast online computation.
Shi et al. (Tue,) studied this question.