End-to-end guarantees for indirect data-driven control of bilinear systems with finite stochastic data

• URL: http://arxiv.org/abs/2409.18010v1
• Date: Thu, 26 Sep 2024 16:19:49 GMT
• Title: End-to-end guarantees for indirect data-driven control of bilinear systems with finite stochastic data
• Authors: Nicolas Chatzikiriakos, Robin Strässer, Frank Allgöwer, Andrea Iannelli,
• Abstract summary: We propose an end-to-end algorithm for indirect data-driven control for bilinear systems with stability guarantees. By means of an extensive numerical study we showcase the interplay between the controller design and the derived identification error bounds.
• Score: 0.0468732641979009
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper we propose an end-to-end algorithm for indirect data-driven control for bilinear systems with stability guarantees. We consider the case where the collected i.i.d. data is affected by probabilistic noise with possibly unbounded support and leverage tools from statistical learning theory to derive finite sample identification error bounds. To this end, we solve the bilinear identification problem by solving a set of linear and affine identification problems, by a particular choice of a control input during the data collection phase. We provide a priori as well as data-dependent finite sample identification error bounds on the individual matrices as well as ellipsoidal bounds, both of which are structurally suitable for control. Further, we integrate the structure of the derived identification error bounds in a robust controller design to obtain an exponentially stable closed-loop. By means of an extensive numerical study we showcase the interplay between the controller design and the derived identification error bounds. Moreover, we note appealing connections of our results to indirect data-driven control of general nonlinear systems through Koopman operator theory and discuss how our results may be applied in this setup.

Related papers

• Assumption-Lean Post-Integrated Inference with Negative Control Outcomes [0.0]
  We introduce a robust post-integrated inference (PII) method that adjusts for latent heterogeneity using negative control outcomes. Our method extends to projected direct effect estimands, accounting for hidden mediators, confounders, and moderators. The proposed doubly robust estimators are consistent and efficient under minimal assumptions and potential misspecification.
  arXiv  Detail & Related papers  (2024-10-07T12:52:38Z)
• A least-square method for non-asymptotic identification in linear switching control [17.938732931331064]
  It is known that the underlying partially-observed linear dynamical system lies within a finite collection of known candidate models. We characterize the finite-time sample complexity of this problem by leveraging recent advances in the non-asymptotic analysis of linear least-square methods. We propose a data-driven switching strategy that identifies the unknown parameters of the underlying system.
  arXiv  Detail & Related papers  (2024-04-11T20:55:38Z)
• DAGnosis: Localized Identification of Data Inconsistencies using Structures [73.39285449012255]
  Identification and appropriate handling of inconsistencies in data at deployment time is crucial to reliably use machine learning models. We use directed acyclic graphs (DAGs) to encode the training set's features probability distribution and independencies as a structure. Our method, called DAGnosis, leverages these structural interactions to bring valuable and insightful data-centric conclusions.
  arXiv  Detail & Related papers  (2024-02-26T11:29:16Z)
• LMI-based Data-Driven Robust Model Predictive Control [0.1473281171535445]
  We propose a data-driven robust linear matrix inequality-based model predictive control scheme that considers input and state constraints. The controller stabilizes the closed-loop system and guarantees constraint satisfaction.
  arXiv  Detail & Related papers  (2023-03-08T18:20:06Z)
• Causality-Based Multivariate Time Series Anomaly Detection [63.799474860969156]
  We formulate the anomaly detection problem from a causal perspective and view anomalies as instances that do not follow the regular causal mechanism to generate the multivariate data. We then propose a causality-based anomaly detection approach, which first learns the causal structure from data and then infers whether an instance is an anomaly relative to the local causal mechanism. We evaluate our approach with both simulated and public datasets as well as a case study on real-world AIOps applications.
  arXiv  Detail & Related papers  (2022-06-30T06:00:13Z)
• Robust Data-Driven Predictive Control using Reachability Analysis [6.686241050151697]
  We present a robust data-driven control scheme for unknown linear systems with a bounded process and measurement noise. The data-driven reachable regions are computed based on only noisy input-output data of a trajectory of the system. In the noise-free case, we prove that the presented purely data-driven control scheme results in an equivalent closed-loop behavior to a nominal model predictive control scheme.
  arXiv  Detail & Related papers  (2021-03-25T19:55:15Z)
• Non-Episodic Learning for Online LQR of Unknown Linear Gaussian System [0.0]
  We propose an online non-episodic algorithm that gains knowledge about the system from a single trajectory. We characterize the almost sure convergence rates of identification and control, and reveal an optimal trade-off between exploration and exploitation.
  arXiv  Detail & Related papers  (2021-03-24T15:51:28Z)
• Sparse PCA via $l_{2,p}$-Norm Regularization for Unsupervised Feature Selection [138.97647716793333]
  We propose a simple and efficient unsupervised feature selection method, by combining reconstruction error with $l_2,p$-norm regularization. We present an efficient optimization algorithm to solve the proposed unsupervised model, and analyse the convergence and computational complexity of the algorithm theoretically.
  arXiv  Detail & Related papers  (2020-12-29T04:08:38Z)
• The Impact of Data on the Stability of Learning-Based Control- Extended Version [63.97366815968177]
  We propose a Lyapunov-based measure for quantifying the impact of data on the certifiable control performance. By modeling unknown system dynamics through Gaussian processes, we can determine the interrelation between model uncertainty and satisfaction of stability conditions.
  arXiv  Detail & Related papers  (2020-11-20T19:10:01Z)
• Learning while Respecting Privacy and Robustness to Distributional Uncertainties and Adversarial Data [66.78671826743884]
  The distributionally robust optimization framework is considered for training a parametric model. The objective is to endow the trained model with robustness against adversarially manipulated input data. Proposed algorithms offer robustness with little overhead.
  arXiv  Detail & Related papers  (2020-07-07T18:25:25Z)
• How Training Data Impacts Performance in Learning-based Control [67.7875109298865]
  This paper derives an analytical relationship between the density of the training data and the control performance. We formulate a quality measure for the data set, which we refer to as $rho$-gap. We show how the $rho$-gap can be applied to a feedback linearizing control law.
  arXiv  Detail & Related papers  (2020-05-25T12:13:49Z)

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.