Data-driven verification of system theoretic properties for nonlinear systems

PN 4-2 (II)

Project description

During the first funding phase (PN 4-2 “Determining system theoretic properties from input-output data”), we successfully showed that analyzing system theoretic properties, as the operator gain or passivity, from measured trajectories provides valuable insight into the unknown system and allows for a data-driven controller design by the direct application of well-known feedback theorems. However, the suggested approaches are limited to linear systems while many practical applications are nonlinear, and hence more challenging. To address this restriction, we develop within this project a broad framework for determining system properties from measured trajectories with mathematical rigorous guarantees while focusing on general nonlinear systems. One approach is a combination of polynomial approximation and robust control techniques. The system properties that shall be investigated comprise generally dissipativity, IQCs, and incremental properties, due to their special relevance in controller design for unknown plants. Within the framework, we plan to provide offline methods that learn from measured tuples in storage, as well as online schemes where we actively perform simulations or experiments to generate specific data. Pivotal questions underlying this investigation are: (i) how can we obtain rigorous mathematical guarantees on the system properties for very broad classes of systems, (ii) how can we reduce the number of required data samples, (iii) how can prior knowledge of the system be incorporated into the respective schemes. This framework, in turn, constitutes a fertile soil for applications in soft robotics, where complex system behaviour poses almost insurmountable obstacles for model-based control theory.

Project information

Project title Data-driven verification of system theoretic properties for nonlinear systems
Project leaders Frank Allgöwer (David Remy)
Project staff Robin Strässer, doctoral researcher (since July 2024)
Tim Martin, doctoral researcher (until June 2024)
Project duration September 2022 - Dezember 2025
Project number PN 4-2 (II)

Publications PN 4-2 and PN 4-2 (II)

  1. 2025

    1. R. Strässer, M. Schaller, K. Worthmann, J. Berberich, and F. Allgöwer, “Koopman-based feedback design with stability guarantees,” IEEE Transactions on Automatic Control, vol. 70, Art. no. 1, 2025, doi: 10.1109/TAC.2024.3425770.
    2. R. Strässer, S. Schlor, and F. Allgöwer, “Decrypting Nonlinearity: Koopman Interpretation and Analysis of Cryptosystems,” Automatica, vol. 173, p. 112022, 2025, doi: 10.1016/j.automatica.2024.112022.

  2. 2023

    1. R. Strässer, J. Berberich, and F. Allgöwer, “Control of bilinear systems using gain-scheduling: Stability and performance guarantees,” in 62nd IEEE Conference on Decision and Control (CDC), Singapore, Singapore, 2023, pp. 4674–4681. doi: 10.1109/CDC49753.2023.10384021.
    2. R. Strässer, J. Berberich, and F. Allgöwer, “Robust data-driven control for nonlinear systems using the Koopman operator,” in Proceedings of the 22nd IFAC World Congress, 2023, pp. 2257–2262. doi: https://doi.org/10.1016/j.ifacol.2023.10.1190.
    3. T. Martin and F. Allgöwer, “Data-driven inference on optimal input-output properties of polynomial systems with focus on nonlinearity measures,” IEEE Transactions on Automatic Control, vol. 68, Art. no. 5, 2023, doi: 10.1109/TAC.2022.3226652.
    4. T. Martin and F. Allgöwer, “Data-driven system analysis of nonlinear systems using polynomial approximation,” IEEE Trans. Automat. Control (early access), 2023, doi: 10.1109/TAC.2023.3321212.
    5. T. Martin, T. B. Schön, and F. Allgöwer, “Guarantees for data-driven control of nonlinear systems using semidefinite programming: A survey,” Annual Reviews in Control, vol. 56, p. 100911, 2023, doi: 10.1016/j.arcontrol.2023.100911.
    6. V. Wagner, R. Strässer, F. Allgöwer, and N. E. Radde, “A provably convergent control closure scheme for the Method of Moments of the Chemical Master Equation,” Journal of Chemical Theory and Computation, vol. 19, Art. no. 24, Dec. 2023, doi: https://doi.org/10.1021/acs.jctc.3c00548.
    7. A. Alanwar, A. Koch, F. Allgöwer, and F. H. Johansson, “Data-Driven Reachability Analysis from Noisy Data,” IEEE Transactions on Automatic Control, pp. 1–16, 2023, doi: 10.1109/TAC.2023.3257167.

  3. 2022

    1. T. Martin and F. Allgöwer, “Determining dissipativity for nonlinear systems from noisy data using Taylor polynomial approximation,” in Proc. American Control Conf. (ACC), Atlanta, GA, USA, 2022, pp. 1432–1437.

  4. 2021

    1. A. Alanwar, A. Koch, F. Allgöwer, and K. H. Johansson, “Data-Driven Reachability Analysis Using Matrix Zonotopes,” in Proceedings of the 3rd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research, vol. 144. 2021, pp. 163–175.
    2. N. Wieler, J. Berberich, A. Koch, and F. Allgöwer, “Data-Driven Controller Design via Finite-Horizon Dissipativity,” in Proceedings of the 3rd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research, vol. 144. PMLR, 2021, pp. 287–298.
    3. A. Koch, J. Berberich, and F. Allgöwer, “Provably robust verification of dissipativity properties from data,” IEEE Transactions on Automatic Control, vol. 67, Art. no. 8, 2021, doi: 10.1109/TAC.2021.3116179.
    4. A. Koch, J. M. Montenbruck, and F. Allgöwer, “Sampling Strategies for Data-Driven Inference of Input-Output System Properties,” IEEE Transactions On Automatic Control, vol. 66, pp. 1144–1159, 2021, doi: 10.1109/TAC.2020.2994894.
    5. A. Koch, J. Berberich, J. Köhler, and F. Allgöwer, “Determining optimal input–output properties: A data-driven approach,” Automatica, vol. 134, p. 109906, 2021, doi: https://doi.org/10.1016/j.automatica.2021.109906.
    6. T. Martin and F. Allgöwer, “Dissipativity verification with guarantees for polynomial systems from noisy input-state data,” IEEE Control Systems Letters, vol. 5, Art. no. 4, 2021, doi: 10.1109/LCSYS.2020.3037842.

  5. 2020

    1. T. Martin, A. Koch, and F. Allgöwer, “Data-driven surrogate models for LTI systems via saddle-point dynamics,” in Proc. 21st IFAC World Congress, Berlin, Germany, 2020, pp. 971–976. doi: 10.1016/j.ifacol.2020.12.1261.
    2. T. Martin and F. Allgöwer, “Iterative data-driven inference of nonlinearity measures via successive graph approximation,” in Proceedings 59th IEEE Conference Decision and Control (CDC), Jeju, South Korea, 2020, pp. 4760–4765. doi: 10.1109/CDC42340.2020.9304285.
    3. D. Persson, A. Koch, and F. Allgöwer, “Probabilistic H2-norm estimation via Gaussian process system identification,” in Proceedings 21st IFAC World Congress, Berlin, Germany, 2020, pp. 431–436. doi: 10.1016/j.ifacol.2020.12.211.
    4. A. Koch, J. Berberich, and F. Allgöwer, “Verifying dissipativity properties from noise-corrupted input-state data,” in Proceedings 59th IEEE Conference on Decision and Control (CDC), Jeju, South Korea, 2020, pp. 616–621. doi: 10.1109/CDC42340.2020.9304380.

  6. 2019

    1. T. Martin and F. Allgöwer, “Nonlinearity Measures for Data-Driven System Analysis and Control,” in Proc. 58th IEEE Conf. Decision and Control (CDC), Nice, France, 2019, pp. 3605–3610. doi: 10.1109/CDC40024.2019.9029804.
    2. A. Romer, J. Berberich, J. Köhler, and F. Allgöwer, “One-shot verification of dissipativity properties from input-output data,” IEEE Control Systems Letters, vol. 3, pp. 709–714, 2019, doi: 10.1109/LCSYS.2019.2917162.

  7. 2018

    1. A. Romer, J. M. Montenbruck, and F. Allgöwer, “Data-driven inference of conic relations via saddle-point dynamics,” in Proceedings 9th IFAC Symposium Robust Control Design (ROCOND), Florianópolis, Brazil, 2018, pp. 586–591. doi: 10.1016/j.ifacol.2018.11.139.
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