(59g) Modeling and Predictive Control of Hybrid Dynamical Systems Using Machine Learning Methods

Hybrid dynamical systems refer to a class of systems that exhibit both continuous and discrete dynamics [1]. The combination of continuous and discrete dynamics in hybrid dynamical systems makes it challenging to design controllers and analyze closed-loop stability. The asymptotic stability of hybrid dynamical systems with respect to a compact set has been developed in [2, 3] using model predictive control (MPC) under the assumption that an accurate process model can be developed based on the fundamental physicochemical mechanisms of the system (e.g., using first-principles modeling approaches). However, it is generally difficult to gain full physicochemical knowledge for a complex hybrid dynamical system, which poses challenges to the development of first-principles modes. To this end, machine learning techniques, such as recurrent neural networks (RNNs), have emerged as a promising alternative in modeling complex and nonlinear systems, as they can capture nonlinear dynamics using time-series data. RNNs have been recently used to derive an accurate prediction model for MPC (RNN-MPC), and have achieved great success in controlling nonlinear processes under RNN-MPC [4, 5]. However, at this stage, modeling of hybrid dynamical systems using RNNs has not been studied. Additionally, closed-loop stability analysis of hybrid dynamical systems under RNN-MPC has not been investigated.

Motivated by the above considerations, in this work, we aim to develop RNN models for hybrid dynamical systems and design RNN-based MPC schemes with closed-loop stability guarantees. Specifically, we first present the development of two RNN models for approximating continuous and discrete dynamics of hybrid dynamical system, respectively. A unified hybrid RNN model is then constructed by integrating the two RNN models to capture both continuous and discrete dynamics. Subsequently, an RNN-based MPC scheme is developed to stabilize the hybrid dynamical system, for which sufficient conditions are derived to guarantee closed-loop stability of hybrid dynamical systems under RNN-MPC. Finally, we use two case studies: a bouncing ball model and a nonlinear chemical process, to demonstrate the open-loop and closed-loop performance of hybrid dynamical systems under the proposed RNN-MPC scheme.

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[5] C. Hu, Y. Cao, and Z. Wu. Online machine learning modeling and predictive control of nonlinear systems with scheduled mode transitions. AIChE Journal, 69:e17882, 2023.