LMI-based Data-Driven Robust Model Predictive Control

• URL: http://arxiv.org/abs/2303.04777v1
• Date: Wed, 8 Mar 2023 18:20:06 GMT
• Title: LMI-based Data-Driven Robust Model Predictive Control
• Authors: Hoang Hai Nguyen, Maurice Friedel, Rolf Findeisen
• Abstract summary: 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.
• Score: 0.1473281171535445
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Predictive control, which is based on a model of the system to compute the applied input optimizing the future system behavior, is by now widely used. If the nominal models are not given or are very uncertain, data-driven model predictive control approaches can be employed, where the system model or input is directly obtained from past measured trajectories. Using a data informativity framework and Finsler's lemma, we propose a data-driven robust linear matrix inequality-based model predictive control scheme that considers input and state constraints. Using these data, we formulate the problem as a semi-definite optimization problem, whose solution provides the matrix gain for the linear feedback, while the decisive variables are independent of the length of the measurement data. The designed controller stabilizes the closed-loop system asymptotically and guarantees constraint satisfaction. Numerical examples are conducted to illustrate the method.

Related papers

• Data-driven Bayesian State Estimation with Compressed Measurement of Model-free Process using Semi-supervised Learning [57.04370580292727]
  The research topic is: data-driven Bayesian state estimation with compressed measurement (BSCM) of model-free process. The dimension of the temporal measurement vector is lower than the dimension of the temporal state vector to be estimated. Two existing unsupervised learning-based data-driven methods fail to address the BSCM problem for model-free process. We develop a semi-supervised learning-based DANSE method, referred to as SemiDANSE.
  arXiv  Detail & Related papers  (2024-07-10T05:03:48Z)
• 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)
• 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)
• 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)
• 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)
• 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)
• Gaussian Process-based Min-norm Stabilizing Controller for Control-Affine Systems with Uncertain Input Effects and Dynamics [90.81186513537777]
  We propose a novel compound kernel that captures the control-affine nature of the problem. We show that this resulting optimization problem is convex, and we call it Gaussian Process-based Control Lyapunov Function Second-Order Cone Program (GP-CLF-SOCP)
  arXiv  Detail & Related papers  (2020-11-14T01:27:32Z)
• 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)
• 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)
• Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations [0.0]
  This work derives a residual-based a posteriori error estimator for reduced models learned with non-intrusive model reduction. It is shown that quantities that are necessary for the error estimator can be either obtained exactly as the solutions of least-squares problems in a non-intrusive way.
  arXiv  Detail & Related papers  (2020-05-12T16:08:05Z)
• Technical Report: Adaptive Control for Linearizable Systems Using On-Policy Reinforcement Learning [41.24484153212002]
  This paper proposes a framework for adaptively learning a feedback linearization-based tracking controller for an unknown system. It does not require the learned inverse model to be invertible at all instances of time. A simulated example of a double pendulum demonstrates the utility of the proposed theory.
  arXiv  Detail & Related papers  (2020-04-06T15:50:31Z)

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.