Recurrent Neural Network Training with Convex Loss and Regularization Functions by Extended Kalman Filtering

• URL: http://arxiv.org/abs/2111.02673v1
• Date: Thu, 4 Nov 2021 07:49:15 GMT
• Title: Recurrent Neural Network Training with Convex Loss and Regularization Functions by Extended Kalman Filtering
• Authors: Alberto Bemporad
• Abstract summary: We show that the learning method outperforms gradient descent in a nonlinear system identification benchmark. We also explore the use of the algorithm in data-driven nonlinear model predictive control and its relation with disturbance models for offset-free tracking.
• Score: 0.20305676256390928
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate the use of extended Kalman filtering to train recurrent neural networks for data-driven nonlinear, possibly adaptive, model-based control design. We show that the approach can be applied to rather arbitrary convex loss functions and regularization terms on the network parameters. We show that the learning method outperforms stochastic gradient descent in a nonlinear system identification benchmark and in training a linear system with binary outputs. We also explore the use of the algorithm in data-driven nonlinear model predictive control and its relation with disturbance models for offset-free tracking.

Related papers

• Identification For Control Based on Neural Networks: Approximately Linearizable Models [42.15267357325546]
  This work presents a control-oriented identification scheme for efficient control design and stability analysis of nonlinear systems. Neural networks are used to identify a discrete-time nonlinear state-space model to approximate time-domain input-output behavior. The network is constructed such that the identified model is approximately linearizable by feedback, ensuring that the control law trivially follows from the learning stage.
  arXiv  Detail & Related papers  (2024-09-24T08:31:22Z)
• Koopman-based Deep Learning for Nonlinear System Estimation [1.3791394805787949]
  We present a novel data-driven linear estimator based on Koopman operator theory to extract meaningful finite-dimensional representations of complex non-linear systems. Our estimator is also adaptive to a diffeomorphic transformation of the estimated nonlinear system, which enables it to compute optimal state estimates without re-learning.
  arXiv  Detail & Related papers  (2024-05-01T16:49:54Z)
• Data-driven Nonlinear Model Reduction using Koopman Theory: Integrated Control Form and NMPC Case Study [56.283944756315066]
  We propose generic model structures combining delay-coordinate encoding of measurements and full-state decoding to integrate reduced Koopman modeling and state estimation. A case study demonstrates that our approach provides accurate control models and enables real-time capable nonlinear model predictive control of a high-purity cryogenic distillation column.
  arXiv  Detail & Related papers  (2024-01-09T11:54:54Z)
• Kalman Filter for Online Classification of Non-Stationary Data [101.26838049872651]
  In Online Continual Learning (OCL) a learning system receives a stream of data and sequentially performs prediction and training steps. We introduce a probabilistic Bayesian online learning model by using a neural representation and a state space model over the linear predictor weights. In experiments in multi-class classification we demonstrate the predictive ability of the model and its flexibility to capture non-stationarity.
  arXiv  Detail & Related papers  (2023-06-14T11:41:42Z)
• Low-rank extended Kalman filtering for online learning of neural networks from streaming data [71.97861600347959]
  We propose an efficient online approximate Bayesian inference algorithm for estimating the parameters of a nonlinear function from a potentially non-stationary data stream. The method is based on the extended Kalman filter (EKF), but uses a novel low-rank plus diagonal decomposition of the posterior matrix. In contrast to methods based on variational inference, our method is fully deterministic, and does not require step-size tuning.
  arXiv  Detail & Related papers  (2023-05-31T03:48:49Z)
• Non-linear manifold ROM with Convolutional Autoencoders and Reduced Over-Collocation method [0.0]
  Non-affine parametric dependencies, nonlinearities and advection-dominated regimes of the model of interest can result in a slow Kolmogorov n-width decay. We implement the non-linear manifold method introduced by Carlberg et al [37] with hyper-reduction achieved through reduced over-collocation and teacher-student training of a reduced decoder. We test the methodology on a 2d non-linear conservation law and a 2d shallow water models, and compare the results obtained with a purely data-driven method for which the dynamics is evolved in time with a long-short term memory network
  arXiv  Detail & Related papers  (2022-03-01T11:16:50Z)
• KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics [84.18625250574853]
  We present KalmanNet, a real-time state estimator that learns from data to carry out Kalman filtering under non-linear dynamics. We numerically demonstrate that KalmanNet overcomes nonlinearities and model mismatch, outperforming classic filtering methods.
  arXiv  Detail & Related papers  (2021-07-21T12:26:46Z)
• Neural Dynamic Mode Decomposition for End-to-End Modeling of Nonlinear Dynamics [49.41640137945938]
  We propose a neural dynamic mode decomposition for estimating a lift function based on neural networks. With our proposed method, the forecast error is backpropagated through the neural networks and the spectral decomposition. Our experiments demonstrate the effectiveness of our proposed method in terms of eigenvalue estimation and forecast performance.
  arXiv  Detail & Related papers  (2020-12-11T08:34:26Z)
• Derivative-Based Koopman Operators for Real-Time Control of Robotic Systems [14.211417879279075]
  This paper presents a generalizable methodology for data-driven identification of nonlinear dynamics that bounds the model error. We construct a Koopman operator-based linear representation and utilize Taylor series accuracy analysis to derive an error bound. When combined with control, the Koopman representation of the nonlinear system has marginally better performance than competing nonlinear modeling methods.
  arXiv  Detail & Related papers  (2020-10-12T15:15:13Z)
• Logarithmic Regret Bound in Partially Observable Linear Dynamical Systems [91.43582419264763]
  We study the problem of system identification and adaptive control in partially observable linear dynamical systems. We present the first model estimation method with finite-time guarantees in both open and closed-loop system identification. We show that AdaptOn is the first algorithm that achieves $textpolylogleft(Tright)$ regret in adaptive control of unknown partially observable linear dynamical systems.
  arXiv  Detail & Related papers  (2020-03-25T06:00:33Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.