Derivative-Free Data-Driven Control of Continuous-Time Linear Time-Invariant Systems
Abstract: This paper develops a data-driven stabilization method for continuous-time linear time-invariant systems with theoretical guarantees and no need for signal derivatives. The framework, based on linear matrix inequalities (LMIs), is illustrated in the state-feedback and single-input single-output output-feedback scenarios. Similar to discrete-time approaches, we rely solely on input and state/output measurements. To avoid differentiation, we employ low-pass filters of the available signals that, rather than approximating the derivatives, reconstruct a non-minimal realization of the plant. With access to the filter states and their derivatives, we can solve LMIs derived from sample batches of the available signals to compute a dynamic controller that stabilizes the plant. The effectiveness of the framework is showcased through numerical examples.
- R. S. Sutton, “Reinforcement learning: An introduction,” A Bradford Book, 2018.
- C. De Persis and P. Tesi, “Formulas for data-driven control: Stabilization, optimality, and robustness,” IEEE Transactions on Automatic Control, vol. 65, no. 3, pp. 909–924, 2020.
- H. J. van Waarde, M. K. Camlibel, and M. Mesbahi, “From noisy data to feedback controllers: Nonconservative design via a matrix S-lemma,” IEEE Transactions on Automatic Control, vol. 67, no. 1, pp. 162–175, 2020.
- A. Bisoffi, C. De Persis, and P. Tesi, “Data-based stabilization of unknown bilinear systems with guaranteed basin of attraction,” Systems & Control Letters, vol. 145, p. 104788, 2020.
- B. Nortmann and T. Mylvaganam, “Data-driven control of linear time-varying systems,” in 2020 59th IEEE Conference on Decision and Control. IEEE, 2020, pp. 3939–3944.
- C. De Persis and P. Tesi, “Low-complexity learning of linear quadratic regulators from noisy data,” Automatica, vol. 128, p. 109548, 2021.
- F. Dörfler, P. Tesi, and C. De Persis, “On the certainty-equivalence approach to direct data-driven LQR design,” IEEE Transactions on Automatic Control, vol. 68, no. 12, pp. 7989–7996, 2023.
- J. Berberich, C. W. Scherer, and F. Allgöwer, “Combining prior knowledge and data for robust controller design,” IEEE Transactions on Automatic Control, vol. 68, no. 8, pp. 4618–4633, 2022.
- H. J. Van Waarde, J. Eising, H. L. Trentelman, and M. K. Camlibel, “Data informativity: A new perspective on data-driven analysis and control,” IEEE Transactions on Automatic Control, vol. 65, no. 11, pp. 4753–4768, 2020.
- J. Berberich, S. Wildhagen, M. Hertneck, and F. Allgöwer, “Data-driven analysis and control of continuous-time systems under aperiodic sampling,” IFAC-PapersOnLine, vol. 54, no. 7, pp. 210–215, 2021.
- J. Miller and M. Sznaier, “Data-driven gain scheduling control of linear parameter-varying systems using quadratic matrix inequalities,” IEEE Control Systems Letters, vol. 7, pp. 835–840, 2022.
- J. Eising and J. Cortes, “When sampling works in data-driven control: Informativity for stabilization in continuous time,” IEEE Transactions on Automatic Control, 2024.
- M. Bianchi, S. Grammatico, and J. Cortés, “Data-driven stabilization of switched and constrained linear systems,” Automatica, vol. 171, p. 111974, 2025.
- C. De Persis, R. Postoyan, and P. Tesi, “Event-triggered control from data,” IEEE Transactions on Automatic Control, vol. 69, no. 6, pp. 3780–3795, 2023.
- N. Nordström and S. S. Sastry, “Persistency of excitation in possibly unstable continuous time systems and parameter convergence in adaptive identification,” IFAC Proceedings Volumes, vol. 20, no. 2, pp. 347–352, 1987.
- J. Löfberg, “YALMIP : A toolbox for modeling and optimization in MATLAB,” in In Proceedings of the CACSD Conference, Taipei, Taiwan, 2004.
- G. C. Walsh and H. Ye, “Scheduling of networked control systems,” IEEE control systems magazine, vol. 21, no. 1, pp. 57–65, 2001.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.