Deep Operator Neural Network Model Predictive Control

In this paper, we consider the design of model predictive control (MPC) algorithms based on deep operator neural networks (DeepONets) [1]. These neural networks are capable of accurately approximating real- and complex-valued solutions [2] of continuous-time nonlinear systems without relying on recurrent architectures. The DeepONet architecture is made up of two feedforward neural networks: the branch network, which encodes the input function space, and the trunk network, which represents dependencies on temporal variables or initial conditions. Utilizing the original DeepONet architecture [1] as a predictor within MPC for Multi-Input Multi-Output (MIMO) systems requires multiple branch networks, to generate multi-output predictions, one for each input. Moreover, to predict multiple time steps into the future, the network has to be evaluated multiple times. Motivated by this, we introduce a multi-step DeepONet (MS-DeepONet) architecture that computes in one-shot multi-step predictions of system outputs from multi-step input sequences, which is better suited for MPC. We prove that the MS-DeepONet is a universal approximator in terms of multi-step sequence prediction. Additionally, we develop automated hyperparameter selection strategies and implement MPC frameworks using both the standard DeepONet and the proposed MS-DeepONet architectures in PyTorch. We compare MS-DeepONet, standard DeepONet, and LSTM-based controllers on learning and predictive control tasks for the Van der Pol oscillator and the quadruple tank process. The MS-DeepONet is also evaluated on a challenging cart–pendulum system, where it successfully learns swing-up and stabilization policies. Across the examples, MS-DeepONet outperforms standard DeepONet in prediction accuracy and control performance, and achieves significantly lower computation times than Long Short-Term Memory (LSTM) based MPC. The code is publicly available on: https://github.com/todejong/Deep-Operator-Neural-Network-Model-Predictive-Control.