Machine Learning Modeling of Nonlinear Processes with Lyapunov Stability Guarantees

Machine learning (ML) methods such as neural networks provide an efficient way to build nonlinear dynamic models from data that can be used in the model predictive control system. In this work, we develop - for the first time - the method of ML modeling of nonlinear processes with Lyapunov stability guarantees, and the theory of its generalization performance and closed-loop stability. By designing a novel loss function that accounts for Lyapunov stability conditions in the training phase, the resulting Lyapunov-stable neural network (LSNN) is able to capture the nonlinear dynamics and guarantee closed-loop stability when incorporated in a stabilizing controller simultaneously. Provable closed-loop stability properties are derived based on the analysis of its generalization performance using statistical learning theory. Finally, a chemical reactor example is used to demonstrate the efficacy of the proposed ML modeling method.