Physics-Constrained Taylor Neural Networks for Learning and Control of Dynamical Systems

TL;DR

The paper tackles data-driven dynamical system identification while preserving physical properties by introducing Monotonic Taylor Neural Networks (MTNN) that learn the first-order derivative via a Taylor expansion. Monotonicity and convexity are enforced through architecture-based constraints or loss-based regularization, enabling physically consistent predictions for systems with exogenous inputs and multiple states/outputs. The approach yields quantum improvements over unconstrained Taylor NN and Min-Max models in HVAC system identification and enables a robust model predictive controller for TCLab, with successful tracking even when operating outside the training data range. Overall, MTNN provides a practical, physics-informed route for learning and controlling nonlinear dynamical systems, especially MIMO systems with external inputs.

Abstract

Data-driven approaches are increasingly popular for identifying dynamical systems due to improved accuracy and availability of sensor data. However, relying solely on data for identification does not guarantee that the identified systems will maintain their physical properties or that the predicted models will generalize well. In this paper, we propose a novel method for system identification by integrating a neural network as the first-order derivative of a Taylor series expansion instead of learning a dynamical function directly. This approach, called Monotonic Taylor Neural Networks (MTNN), aims to ensure monotonic properties of dynamical systems by constraining the conditions for the output of the neural networks model to be either always non-positive or non-negative. These conditions are constructed in two ways: by designing a new neural network architecture or by regularizing the loss function for training. The proposed method demonstrates better performance compared to methods without constraints on the monotonic properties of the systems when tested with experimental data from two real-world systems, including HVAC and TCLab. Furthermore, MTNN shows good performance in an actual control application when using a model predictive controller for a nonlinear MIMO system, illustrating the practical applications of this method.

Figures (4)

• Figure 1: Neural network of first-order derivative
• Figure 2: Monotonic property constrain
• Figure 3: MPC controller for MTNN model
• Figure 4: Measured temperature and control input in real TCLab using MPC