Nonlinear Discrete-time Systems' Identification without Persistence of Excitation: A Finite-time Concurrent Learning

• URL: http://arxiv.org/abs/2112.07765v1
• Date: Tue, 14 Dec 2021 22:19:20 GMT
• Title: Nonlinear Discrete-time Systems' Identification without Persistence of Excitation: A Finite-time Concurrent Learning
• Authors: Farzaneh Tatari, Chiristos Panayiotou, Marios Polycarpou
• Abstract summary: A finite-time concurrent learning approach is presented to approximate the uncertainties of the discrete-time nonlinear systems. Rigorous proofs guarantee the finite-time convergence of the estimated parameters to their optimal values.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper deals with the problem of finite-time learning for unknown discrete-time nonlinear systems' dynamics, without the requirement of the persistence of excitation. A finite-time concurrent learning approach is presented to approximate the uncertainties of the discrete-time nonlinear systems in an on-line fashion by employing current data along with recorded experienced data satisfying an easy-to-check rank condition on the richness of the recorded data which is less restrictive in comparison with persistence of excitation condition. Rigorous proofs guarantee the finite-time convergence of the estimated parameters to their optimal values based on a discrete-time Lyapunov analysis. Compared with the existing work in the literature, simulation results illustrate that the proposed method can timely and precisely approximate the uncertainties.

Related papers

• Statistical Inference for Temporal Difference Learning with Linear Function Approximation [62.69448336714418]
  Temporal Difference (TD) learning, arguably the most widely used for policy evaluation, serves as a natural framework for this purpose. In this paper, we study the consistency properties of TD learning with Polyak-Ruppert averaging and linear function approximation, and obtain three significant improvements over existing results.
  arXiv  Detail & Related papers  (2024-10-21T15:34:44Z)
• Learning Unstable Continuous-Time Stochastic Linear Control Systems [0.0]
  We study the problem of system identification for continuous-time dynamics, based on a single finite-length state trajectory. We present a method for estimating the possibly unstable open-loop matrix by employing properly randomized control inputs. We establish theoretical performance guarantees showing that the estimation error decays with trajectory length, a measure of excitability, and the signal-to-noise ratio.
  arXiv  Detail & Related papers  (2024-09-17T16:24:51Z)
• A projected nonlinear state-space model for forecasting time series signals [0.6537685198688538]
  We propose a fast algorithm to learn and forecast nonlinear dynamics from noisy time series data. A key feature of the proposed model is kernel functions applied to projected lines, enabling fast capture of nonlinearities in the latent dynamics.
  arXiv  Detail & Related papers  (2023-11-22T09:05:37Z)
• Probabilistic Learning of Multivariate Time Series with Temporal Irregularity [25.91078012394032]
  temporal irregularities, including nonuniform time intervals and component misalignment. We develop a conditional flow representation to non-parametrically represent the data distribution, which is typically non-Gaussian. The broad applicability and superiority of the proposed solution are confirmed by comparing it with existing approaches through ablation studies and testing on real-world datasets.
  arXiv  Detail & Related papers  (2023-06-15T14:08:48Z)
• Non-Parametric Learning of Stochastic Differential Equations with Non-asymptotic Fast Rates of Convergence [65.63201894457404]
  We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of non-linear differential equations. The key idea essentially consists of fitting a RKHS-based approximation of the corresponding Fokker-Planck equation to such observations.
  arXiv  Detail & Related papers  (2023-05-24T20:43:47Z)
• Bayesian Spline Learning for Equation Discovery of Nonlinear Dynamics with Quantified Uncertainty [8.815974147041048]
  We develop a novel framework to identify parsimonious governing equations of nonlinear (spatiotemporal) dynamics from sparse, noisy data with quantified uncertainty. The proposed algorithm is evaluated on multiple nonlinear dynamical systems governed by canonical ordinary and partial differential equations.
  arXiv  Detail & Related papers  (2022-10-14T20:37:36Z)
• Continuous-Time Modeling of Counterfactual Outcomes Using Neural Controlled Differential Equations [84.42837346400151]
  Estimating counterfactual outcomes over time has the potential to unlock personalized healthcare. Existing causal inference approaches consider regular, discrete-time intervals between observations and treatment decisions. We propose a controllable simulation environment based on a model of tumor growth for a range of scenarios.
  arXiv  Detail & Related papers  (2022-06-16T17:15:15Z)
• Pessimistic Q-Learning for Offline Reinforcement Learning: Towards Optimal Sample Complexity [51.476337785345436]
  We study a pessimistic variant of Q-learning in the context of finite-horizon Markov decision processes. A variance-reduced pessimistic Q-learning algorithm is proposed to achieve near-optimal sample complexity.
  arXiv  Detail & Related papers  (2022-02-28T15:39:36Z)
• 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)
• Concurrent Learning Based Tracking Control of Nonlinear Systems using Gaussian Process [2.7930955543692817]
  This paper demonstrates the applicability of the combination of concurrent learning as a tool for parameter estimation and non-parametric Gaussian Process for online disturbance learning. A control law is developed by using both techniques sequentially in the context of feedback linearization. The closed-loop system stability for the nth-order system is proven using the Lyapunov stability theorem.
  arXiv  Detail & Related papers  (2021-06-02T02:59:48Z)
• Learning Fast Approximations of Sparse Nonlinear Regression [50.00693981886832]
  In this work, we bridge the gap by introducing the Threshold Learned Iterative Shrinkage Algorithming (NLISTA) Experiments on synthetic data corroborate our theoretical results and show our method outperforms state-of-the-art methods.
  arXiv  Detail & Related papers  (2020-10-26T11:31:08Z)

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.