Data-Driven Reachability Analysis Using Matrix Zonotopes

• URL: http://arxiv.org/abs/2011.08472v3
• Date: Sat, 11 Sep 2021 16:05:25 GMT
• Title: Data-Driven Reachability Analysis Using Matrix Zonotopes
• Authors: Amr Alanwar, Anne Koch, Frank Allg\"ower, Karl Henrik Johansson
• Abstract summary: We propose a data-driven reachability analysis approach from noisy data. We first provide an algorithm for over-approximating the reachable set of a linear time-invariant system. We then introduce an extension for Lipschitz nonlinear systems.
• Score: 5.6184230760292175
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we propose a data-driven reachability analysis approach for unknown system dynamics. Reachability analysis is an essential tool for guaranteeing safety properties. However, most current reachability analysis heavily relies on the existence of a suitable system model, which is often not directly available in practice. We instead propose a data-driven reachability analysis approach from noisy data. More specifically, we first provide an algorithm for over-approximating the reachable set of a linear time-invariant system using matrix zonotopes. Then we introduce an extension for Lipschitz nonlinear systems. We provide theoretical guarantees in both cases. Numerical examples show the potential and applicability of the introduced methods.

Related papers

• Information-Theoretic Safe Bayesian Optimization [59.758009422067005]
  We consider a sequential decision making task, where the goal is to optimize an unknown function without evaluating parameters that violate an unknown (safety) constraint. Most current methods rely on a discretization of the domain and cannot be directly extended to the continuous case. We propose an information-theoretic safe exploration criterion that directly exploits the GP posterior to identify the most informative safe parameters to evaluate.
  arXiv  Detail & Related papers  (2024-02-23T14:31:10Z)
• Data-Driven Reachability Analysis of Stochastic Dynamical Systems with Conformal Inference [1.446438366123305]
  We consider data-driven reachability analysis of discrete-time dynamical systems using conformal inference. We focus on learning-enabled control systems with complex closed-loop dynamics.
  arXiv  Detail & Related papers  (2023-09-17T07:23:01Z)
• Robust identification of non-autonomous dynamical systems using stochastic dynamics models [0.0]
  This paper considers the problem of system identification (ID) of linear and nonlinear non-autonomous systems from noisy and sparse data. We propose and analyze an objective function derived from a Bayesian formulation for learning a hidden Markov model. We show that our proposed approach has improved smoothness and inherent regularization that make it well-suited for system ID.
  arXiv  Detail & Related papers  (2022-12-20T16:36:23Z)
• Log Barriers for Safe Black-box Optimization with Application to Safe Reinforcement Learning [72.97229770329214]
  We introduce a general approach for seeking high dimensional non-linear optimization problems in which maintaining safety during learning is crucial. Our approach called LBSGD is based on applying a logarithmic barrier approximation with a carefully chosen step size. We demonstrate the effectiveness of our approach on minimizing violation in policy tasks in safe reinforcement learning.
  arXiv  Detail & Related papers  (2022-07-21T11:14:47Z)
• Koopman operator for time-dependent reliability analysis [0.0]
  We propose an end-to-end deep learning architecture that learns the Koopman observables and then use it for time marching the dynamical response. Unlike purely data-driven approaches, the proposed approach is robust even in the presence of uncertainties.
  arXiv  Detail & Related papers  (2022-03-05T04:57:20Z)
• 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)
• Time varying regression with hidden linear dynamics [74.9914602730208]
  We revisit a model for time-varying linear regression that assumes the unknown parameters evolve according to a linear dynamical system. Counterintuitively, we show that when the underlying dynamics are stable the parameters of this model can be estimated from data by combining just two ordinary least squares estimates.
  arXiv  Detail & Related papers  (2021-12-29T23:37:06Z)
• Learning Stable Koopman Embeddings [9.239657838690228]
  We present a new data-driven method for learning stable models of nonlinear systems. We prove that every discrete-time nonlinear contracting model can be learnt in our framework.
  arXiv  Detail & Related papers  (2021-10-13T05:44:13Z)
• Probabilistic robust linear quadratic regulators with Gaussian processes [73.0364959221845]
  Probabilistic models such as Gaussian processes (GPs) are powerful tools to learn unknown dynamical systems from data for subsequent use in control design. We present a novel controller synthesis for linearized GP dynamics that yields robust controllers with respect to a probabilistic stability margin.
  arXiv  Detail & Related papers  (2021-05-17T08:36:18Z)
• Data-Driven Reachability Analysis from Noisy Data [5.949143454441281]
  We consider the problem of computing reachable sets directly from noisy data without a given system model. Several reachability algorithms are presented, and their accuracy is shown to depend on the underlying system generating the data.
  arXiv  Detail & Related papers  (2021-05-15T14:11:57Z)
• 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.