rapid-communication

Data-driven quadratic stabilization and LQR control of LTI systems

Authors:

Mario SznaierAuthors Info & Claims

Volume 153, Issue C

https://doi.org/10.1016/j.automatica.2023.111041

Published: 01 July 2023 Publication History

Abstract

In this paper, we propose a framework to solve the data-driven quadratic stabilization (DDQS) and the data-driven linear quadratic regulator (DDLQR) problems for both continuous and discrete-time systems. Given noisy input/state measurements and a few priors, we aim to find a state feedback controller guaranteed to quadratically stabilize all systems compatible with the a-priori information and the experimental data. In principle, finding such a controller is a non-convex robust optimization problem. Our main result shows that, by exploiting duality, the problem can be recast into a convex, albeit infinite-dimensional, functional Linear Program. To address the computational complexity entailed in solving this problem, we show that a sequence of increasingly tight finite dimensional semi-definite relaxations can be obtained using sum-of-squares and Putinar’s Positivstellensatz arguments. Finally, we show that these arguments can also be used to find controllers that minimize a worst-case (over all plants in the consistency set) closed-loop H 2 cost. The effectiveness of the proposed algorithm is illustrated through comparisons against existing data-driven methods that handle ℓ ∞ bounded noise.

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Cited By

Liu YXia YHuang J(2024)Data-driven output consensus for a class of discrete-time multiagent systems by reinforcement learning techniquesSignal Processing10.1016/j.sigpro.2024.109547223:COnline publication date: 1-Oct-2024
https://dl.acm.org/doi/10.1016/j.sigpro.2024.109547
Gómez-Múnera JDíaz-Charris LJiménez-Cabas J(2023)Artificial Neural Network to Estimate Deterministic Indices in Control Loop Performance MonitoringIntelligent Human Computer Interaction10.1007/978-3-031-53830-8_14(139-150)Online publication date: 8-Nov-2023
https://dl.acm.org/doi/10.1007/978-3-031-53830-8_14

Index Terms

Data-driven quadratic stabilization and LQR control of LTI systems
1. Mathematics of computing
  1. Mathematical analysis
    1. Mathematical optimization
      1. Continuous optimization
    2. Numerical analysis
2. Theory of computation
  1. Design and analysis of algorithms
    1. Mathematical optimization
      1. Continuous optimization
        Linear programming

Index terms have been assigned to the content through auto-classification.

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Published In

cover image Automatica (Journal of IFAC)

Automatica (Journal of IFAC) Volume 153, Issue C

Jul 2023

485 pages

ISSN:0005-1098

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Elsevier Ltd.

Publisher

Pergamon Press, Inc.

United States

Publication History

Published: 01 July 2023

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Cited By

Liu YXia YHuang J(2024)Data-driven output consensus for a class of discrete-time multiagent systems by reinforcement learning techniquesSignal Processing10.1016/j.sigpro.2024.109547223:COnline publication date: 1-Oct-2024
https://dl.acm.org/doi/10.1016/j.sigpro.2024.109547
Gómez-Múnera JDíaz-Charris LJiménez-Cabas J(2023)Artificial Neural Network to Estimate Deterministic Indices in Control Loop Performance MonitoringIntelligent Human Computer Interaction10.1007/978-3-031-53830-8_14(139-150)Online publication date: 8-Nov-2023
https://dl.acm.org/doi/10.1007/978-3-031-53830-8_14

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