Determining system theoretic properties from input-output data

PN 4-2

Project description

One of the drawbacks of many data-driven control approaches is the lack of guarantees for stability, performance and robustness. Instead of directly learning a controller from data, we therefore suggest learning and analyzing certain system theoretic properties from data in order to leverage this knowledge for controller design. In fact, certain system properties such as the operator gain or passivity properties allow for the direct application of well-known feedback theorems, hence leading to insights to the unknown system and providing guarantees for the closed-loop behavior. Therefore, we aim to develop a broad framework for characterizing such properties of an unknown system solely on the basis of input-output trajectories (i) from storage (offline methods), or (ii) obtained from actively conducting simulations or experiments (online methods). In both scenarios, we aim at approaches that come with provable guarantees for broad classes of system properties. Pivotal questions underlying this investigation are: how can we obtain rigorous mathematical guarantees on the system properties for very broad classes of systems, how can we reduce the number of required input-output data tuples, and how can prior knowledge of the system be incorporated into the respective schemes. This framework, in turn, constitutes a fertile soil for applications in biomechanics and biorobotics, where complex systems and their interactions pose almost insurmountable obstacles for state of the art control theory. This leads us to the last pivotal question: how can we exploit this novel methodology in application fields.

Project information

Project title Determining system theoretic properties from input-output data
Project leader Frank Allgöwer (Syn Schmitt)
Project duration January 2020 - June 2023
Project number PN 4-2

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, no. 1, 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), 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, in Proceedings of the 22nd IFAC World Congress, vol. 56. 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, no. 5, Art. no. 5, 2023, doi: 10.1109/TAC.2022.3226652.
    4. 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.
    5. 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.
    6. 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.
    7. 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, no. 24, Art. no. 24, Dec. 2023, doi: https://doi.org/10.1021/acs.jctc.3c00548.

  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), 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 the 3rd Conference on Learning for Dynamics and Control, 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 the 3rd Conference on Learning for Dynamics and Control, 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, no. 8, 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, no. 4, Art. no. 4, 2021, doi: 10.1109/LCSYS.2020.3037842.

  5. 2020

    1. 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), in Proceedings 59th IEEE Conference Decision and Control (CDC). Jeju, South Korea, 2020, pp. 4760–4765. doi: 10.1109/CDC42340.2020.9304285.
    2. T. Martin, A. Koch, and F. Allgöwer, “Data-driven surrogate models for LTI systems via saddle-point dynamics,” in Proc. 21st IFAC World Congress, in Proc. 21st IFAC World Congress. Berlin, Germany, 2020, pp. 971–976. doi: 10.1016/j.ifacol.2020.12.1261.
    3. D. Persson, A. Koch, and F. Allgöwer, “Probabilistic H2-norm estimation via Gaussian process system identification,” in Proceedings 21st IFAC World Congress, 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), 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), 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), 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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