Relaxed Stability Conditions for Model Predictive Control of Hybrid Dynamical Systems Using Hybrid Recurrent Neural Networks

We propose a Lyapunov-based model predictive control (LMPC) framework that integrates recurrent neural networks (RNNs) for the modeling and control of hybrid dynamical systems. Such systems involve both discrete and continuous dynamics, which are described by difference and differential equations, respectively. Specifically, a unified hybrid RNN is first constructed by integrating two offline-trained RNNs to model discrete-time and continuous-time subsystems, respectively. A key advantage of our approach is that it does not require the model mismatch between the hybrid RNN and the true hybrid system to be sufficiently small for both discrete and continuous dynamics. Under this relaxed modeling error constraint, we develop an LMPC scheme using the initial hybrid RNN, which ensures closed-loop stability for hybrid dynamical systems with some system properties. Subsequently, a Lyapunov function-based online learning strategy is proposed, wherein real-time operational data is utilized to update the hybrid RNN. Finally, the efficacy of the proposed LMPC framework with and without the online learning mechanism of the hybrid RNN is validated through a numerical example involving hybrid dynamics.