Abstract
We present a data-driven dissipative verification method for LTI systems based on using multiple input-output data. We assume that the supply-rate functions have a quadratic difference form corresponding to the general dissipativity notion known in the behavioural framework. We validate our approach in a practical example using a two-degree-of-freedom planar manipulator from Quanser, with which we demonstrate the applicability of multiple datasets over one-shot of data recently proposed in the literature.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Maupong, T., Mayo-Maldonado, J.C., Rapisarda, P.: On Lyapunov functions and data-driven dissipativity. IFAC-PapersOnLine 50(1), 7783–7788 (2017)
Romer, A., Berberich, J., Köhler, J., Allgöwer, F.: One-shot verification of dissipativity properties from input-output data. IEEE Control Syst. Lett. 3(3), 709–714 (2019)
van Waarde, H.J., De Persis, C., Camlibel, M.K., Tesi, P.: Willems’ fundamental lemma for state-space systems and its extension to multiple datasets. IEEE Control Syst. Lett. 4(3), 602–607 (2020)
Markovsky, I., Dörfler, F.: Behavioral systems theory in data-driven analysis, signal processing, and control. Annu. Rev. Control 52, 42–64 (2021)
Rosa, T.E., Jayawardhana, B.: On the one-shot data-driven verification of dissipativity of LTI systems with general quadratic supply rate function. In: Proceedings of the 19th European Control Conference, (Rotterdam), pp. 1291–1296. IEEE (2021)
van Waarde, H.J., Camlibel, M.K., Rapisarda, P., Trentelman, H.L.: Data-driven dissipativity analysis: application of the matrix S-lemma. IEEE Control Syst. Mag. 42(3), 140–149 (2022)
Koch, A., Berberich, J., Allgower, F.: Provably robust verification of dissipativity properties from data. IEEE Trans. Autom. Control (2021)
Van Waarde, H.J., Eising, J., Trentelman, H.L., Camlibel, M.K.: Data informativity: a new perspective on data-driven analysis and control. IEEE Trans. Autom. Control 65(11), 4753–4768 (2020)
Markovsky, I.: Exact system identification with missing data. In: 52nd IEEE Conference on Decision and Control, pp. 151–155. IEEE (2013)
Liu, Z., Hansson, A., Vandenberghe, L.: Nuclear norm system identification with missing inputs and outputs. Syst. Control Lett. 62(8), 605–612 (2013)
Ding, T., Sznaier, M., Camps, O.: A rank minimization approach to fast dynamic event detection and track matching in video sequences. In: 2007 46th IEEE Conference on Decision and Control, pp. 4122–4127. IEEE (2007)
Noh, S., Zoltowski, M.D., Sung, Y., Love, D.J.: Pilot beam pattern design for channel estimation in massive MIMO systems. IEEE J. Sel. Top. Signal Process. 8(5), 787–801 (2014)
Markovsky, I.: A missing data approach to data-driven filtering and control. IEEE Trans. Autom. Control 62(4), 1972–1978 (2016)
Berberich, J., Allgöwer, F.: A trajectory-based framework for data-driven system analysis and control. In: 2020 European Control Conference (ECC), pp. 1365–1370. IEEE (2020)
Lanzon, A., Petersen, I.R.: Stability robustness of a feedback interconnection of systems with negative imaginary frequency response. IEEE Trans. Autom. Control 53(4), 1042–1046 (2008)
Mabrok, M.A., Alyami, M.A., Mahmoud, E.E.: On the dissipativity property of negative imaginary systems. Alex. Eng. J. 60(1), 1403–1410 (2021)
Ouyang, R., Andrieu, V., Jayawardhana, B.: On the characterization of the Duhem hysteresis operator with clockwise input-output dynamics. Syst. Control Lett. 62(3), 286–293 (2013)
Ouyang, R., Jayawardhana, B.: Absolute stability analysis of linear systems with Duhem hysteresis operator. Automatica 50(7), 1860–1866 (2014)
Lei, Q., Munir, M.T., Bao, J., Young, B.: A data-driven fault detection method based on dissipative trajectories. IFAC-PapersOnLine 49(7), 717–722 (2016)
de Oliveira, M.C., Skelton, R.E.: Stability tests for constrained linear systems. In: Perspectives in Robust Control, pp. 241–257. Springer, Berlin (2001)
Trentelman, H., Willems, J.: Every storage function is a state function. Syst. Control Lett. 32(5), 249–259 (1997)
De Persis, C., Tesi, P.: Formulas for data-driven control: stabilization, optimality, and robustness. IEEE Trans. Autom. Control 65(3), 909–924 (2019)
Quanser.: 2 DOF Serial Flexible Joint, Reference Manual. Doc. No. 800, Rev 1 (2013)
Chan-Zheng, C., Borja, P., Scherpen, J.M.: Passivity-based control of mechanical systems with linear damping identification. IFAC-PapersOnLine 54(19), 255–260 (2021)
Ortega, R., Perez, J.A.L., Nicklasson, P.J., Sira-Ramirez, H.J.: Passivity-Based Control of Euler-Lagrange Systems: Mechanical, Electrical and Electromechanical Applications. Springer Science & Business Media (2013)
Löfberg, J.: YALMIP: a toolbox for modeling and optimization in MATLAB, pp. 284–289. Taipei, Taiwan (2004)
ApS, M.: The MOSEK optimization toolbox for MATLAB manual. Version 9.0 (2019)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Rosa, T.E., Jayawardhana, B. (2023). Data-Driven Dissipative Verification of LTI Systems: Multiple Shots of Data, QDF Supply-Rate and Application to a Planar Manipulator. In: Theilliol, D., Korbicz, J., Kacprzyk, J. (eds) Recent Developments in Model-Based and Data-Driven Methods for Advanced Control and Diagnosis. ACD 2022. Studies in Systems, Decision and Control, vol 467. Springer, Cham. https://doi.org/10.1007/978-3-031-27540-1_22
Download citation
DOI: https://doi.org/10.1007/978-3-031-27540-1_22
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-27539-5
Online ISBN: 978-3-031-27540-1
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)