Locality-Preserving Graph Laplacian Manifold Learning Based Model Predictive Control for Three-Phase Inverters

A Spatiotemporal Graph Convolutional Network for Predictive Control With Stability Guarantees

Low-Order Continuous-Time Koopman Operator Learning via Physics-Informed Neural Networks

One of the main objectives in control theory is to obtain a linear representation of inherently nonlinear systems in order to leverage the analytical and theoretical tools developed for linear systems. In this context, the Koopman operator has attracted increasing interest in recent years.Koopman operator theory provides a framework in which nonlinear dynamical systems are represented by a linear operator acting on an infinite-dimensional Hilbert space. Since such an infinite-dimensional representation is not numerically tractable, numerous finite-dimensional approximation methods have been proposed. These approaches typically rely on time-series data and include extended dynamic mode decomposition as well as deep learning–based variants. In this paper, we propose an original machine-learning-based approach for the synthesis of a fixed-dimensional Koopman approximant (lifting) of continuous-time nonlinear systems. A differential state-space representation of the system (as opposed to a recurrent state model) is assumed to be available through its vector field (f). The proposed encoder departs from conventional approaches in that it does not directly output the current latent state, but instead generates samples of the latent trajectory evaluated at user-defined time instants (temporal discretization). This formulation enables the integration into the learning process of Physical & Latent Continuous Losses, enforcing consistency between the physical dynamics and the Koopman dynamics, as well as Physical & Latent Boundary Losses, ensuring consistency with the prescribed initial conditions. In parallel, we introduce a structural stability constraint on the Koopman operator. The effectiveness of the proposed methodology is demonstrated through the analysis and simulation of two polynomial dynamical systems.

Decoder-free operator autoencoder for reduced-order modeling of dynamical systems

A Fourier-enhanced operator autoencoder for decoder-free reconstruction and latent learning of dynamical systems and achieves accuracy comparable to or better than classical AE-based reduced-order models while providing a more efficient latent-to-field reconstruction path.

U-Shaped WaveNet With Adaptive Volterra Neural Networks for Active Noise Control

Deep learning-based active noise control (ANC) algorithms demonstrate superior potential over traditional methods in addressing nonlinear distortion. Although recent deep learning approaches incorporating Volterra Neural Networks (VNNs) have been optimized to tackle nonlinearities, there remains room for further improvement: (1) utilizing element-wise addition in skip connections across different feature processing stages increases the risk of feature aliasing or suppression; (2) directly introducing higher-order terms of the Volterra series is prone to causing overfitting; and (3) models trained under a singular nonlinear condition struggle to adapt to real-world scenarios with varying nonlinearities. To address these issues, this letter proposes a novel time-domain ANC framework. While retaining the modeling capabilities of WaveNet and VNNs, the proposed framework integrates the U-shaped structure and incorporates an adaptive gating mechanism for the higher-order Volterra terms. The proposed method is compared with a state-of-the-art deep learning framework. Additionally, the model is evaluated under several controlled nonlinear conditions, and comprehensive ablation studies are conducted. Simulation results demonstrate that the proposed algorithm outperforms existing end-to-end representative Deep Neural Network (DNN) methods, and ablation studies confirm the effectiveness of the proposed modules.

Hybrid Deep Learning and First-Principles Model for Predictive Control of Solar Direct Steam Generation

Linear Fresnel Reflector (LFR) systems for Direct Steam Generation (DSG) exhibit strong nonlinear and transient dynamics due to diurnal solar variability, making real-time control challenging. To address this, a Gated Recurrent Unit (GRU)-based deep neural network surrogate replaces the computationally intensive first-principles LFR model and is embedded within a Nonlinear Model Predictive Control (NMPC) framework for fast prediction. Trained using scheduled sampling, the surrogate achieves prediction fits of 87.39% for steam quality and 90.55% for LFR outlet pressure. The GRU-based LFR model is integrated with a first-principles Steam Drum (SD) model in a centralized NMPC scheme to regulate steam quality and drum water level. Closed-loop simulations under varying solar insolation with cloud cover demonstrate effective tracking of time-varying setpoints, validating the proposed hybrid predictive control approach.

Data-driven predictive control of nonlinear systems using weighted regularization

This work proposes a data-driven predictive control framework for nonlinear systems that incorporates data column preferences according to their proximity to the current operating point through a weighted norm regularization, thereby localizing the predictor without discarding any data.