Learning Reduced Nonlinear State-Space Models: an Output-Error Based Canonical Approach

• URL: http://arxiv.org/abs/2206.04791v1
• Date: Tue, 19 Apr 2022 06:33:23 GMT
• Title: Learning Reduced Nonlinear State-Space Models: an Output-Error Based Canonical Approach
• Authors: Steeven Janny, Quentin Possamai, Laurent Bako, Madiha Nadri, Christian Wolf
• Abstract summary: We investigate the effectiveness of deep learning in the modeling of dynamic systems with nonlinear behavior. We show its ability to identify three different nonlinear systems. The performances are evaluated in terms of open-loop prediction on test data generated in simulation as well as a real world data-set of unmanned aerial vehicle flight measurements.
• Score: 8.029702645528412
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The identification of a nonlinear dynamic model is an open topic in control theory, especially from sparse input-output measurements. A fundamental challenge of this problem is that very few to zero prior knowledge is available on both the state and the nonlinear system model. To cope with this challenge, we investigate the effectiveness of deep learning in the modeling of dynamic systems with nonlinear behavior by advocating an approach which relies on three main ingredients: (i) we show that under some structural conditions on the to-be-identified model, the state can be expressed in function of a sequence of the past inputs and outputs; (ii) this relation which we call the state map can be modelled by resorting to the well-documented approximation power of deep neural networks; (iii) taking then advantage of existing learning schemes, a state-space model can be finally identified. After the formulation and analysis of the approach, we show its ability to identify three different nonlinear systems. The performances are evaluated in terms of open-loop prediction on test data generated in simulation as well as a real world data-set of unmanned aerial vehicle flight measurements.

Related papers

• 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)
• Gaussian process learning of nonlinear dynamics [0.0]
  We propose a new method that learns nonlinear dynamics through a Bayesian inference of characterizing model parameters. We will discuss the applicability of the proposed method to several typical scenarios for dynamical systems.
  arXiv  Detail & Related papers  (2023-12-19T14:27:26Z)
• Neural Abstractions [72.42530499990028]
  We present a novel method for the safety verification of nonlinear dynamical models that uses neural networks to represent abstractions of their dynamics. We demonstrate that our approach performs comparably to the mature tool Flow* on existing benchmark nonlinear models.
  arXiv  Detail & Related papers  (2023-01-27T12:38:09Z)
• A Priori Denoising Strategies for Sparse Identification of Nonlinear Dynamical Systems: A Comparative Study [68.8204255655161]
  We investigate and compare the performance of several local and global smoothing techniques to a priori denoise the state measurements. We show that, in general, global methods, which use the entire measurement data set, outperform local methods, which employ a neighboring data subset around a local point.
  arXiv  Detail & Related papers  (2022-01-29T23:31:25Z)
• Likelihood-Free Inference in State-Space Models with Unknown Dynamics [71.94716503075645]
  We introduce a method for inferring and predicting latent states in state-space models where observations can only be simulated, and transition dynamics are unknown. We propose a way of doing likelihood-free inference (LFI) of states and state prediction with a limited number of simulations.
  arXiv  Detail & Related papers  (2021-11-02T12:33:42Z)
• A Latent Restoring Force Approach to Nonlinear System Identification [0.0]
  This work suggests an approach based on Bayesian filtering to extract and identify the contribution of an unknown nonlinear term in the system. The approach is demonstrated to be effective in both a simulated case study and on an experimental benchmark dataset.
  arXiv  Detail & Related papers  (2021-09-22T12:21:16Z)
• Supervised DKRC with Images for Offline System Identification [77.34726150561087]
  Modern dynamical systems are becoming increasingly non-linear and complex. There is a need for a framework to model these systems in a compact and comprehensive representation for prediction and control. Our approach learns these basis functions using a supervised learning approach.
  arXiv  Detail & Related papers  (2021-09-06T04:39:06Z)
• Constrained Block Nonlinear Neural Dynamical Models [1.3163098563588727]
  Neural network modules conditioned by known priors can be effectively trained and combined to represent systems with nonlinear dynamics. The proposed method consists of neural network blocks that represent input, state, and output dynamics with constraints placed on the network weights and system variables. We evaluate the performance of the proposed architecture and training methods on system identification tasks for three nonlinear systems.
  arXiv  Detail & Related papers  (2021-01-06T04:27:54Z)
• Data Assimilation Networks [1.5545257664210517]
  Data assimilation aims at forecasting the state of a dynamical system by combining a mathematical representation of the system with noisy observations. We propose a fully data driven deep learning architecture generalizing recurrent Elman networks and data assimilation algorithms. Our architecture achieves comparable performance to EnKF on both the analysis and the propagation of probability density functions of the system state at a given time without using any explicit regularization technique.
  arXiv  Detail & Related papers  (2020-10-19T17:35:36Z)
• Active Learning for Nonlinear System Identification with Guarantees [102.43355665393067]
  We study a class of nonlinear dynamical systems whose state transitions depend linearly on a known feature embedding of state-action pairs. We propose an active learning approach that achieves this by repeating three steps: trajectory planning, trajectory tracking, and re-estimation of the system from all available data. We show that our method estimates nonlinear dynamical systems at a parametric rate, similar to the statistical rate of standard linear regression.
  arXiv  Detail & Related papers  (2020-06-18T04:54:11Z)

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.