A Non-Iterative Approach to Direct Data-Driven Control Design of MIMO LTI Systems

errors-in-variables; multivariable systems; Non-iterative direct data-driven control tuning; set-membership; Control design; Control tuning; Controller parameter; Data-driven control; Error-in-variable; Iterative approach; Multi-variables system; Non-iterative; Set-membership; Computer Science (all); Materials Science (all); Engineering (all)

Abstract :

[en] This paper proposes a non-iterative direct data-driven technique that deals with linear time-invariant (LTI) controller design by directly identifying the controller from input-output data without using plant identification. We define the feasible controller parameter set and formulate the problem of designing a controller to match the behaviour of a given reference model as an equivalent set-membership errors-in-variables problem. Then we design the controller parameters by applying recent results in set-membership errors-in-variables identification. Finally, we analyse the effectiveness of the presented technique through simulation examples and experimental results.

Disciplines :

Electrical & electronics engineering

Author, co-author :

ABUABIAH, Mohammad ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE) ; An-Najah National University, Faculty of Engineering and Information Technology, Mechatronics Engineering Department, Nablus, Palestine

Cerone, Vito ; Politecnico di Torino, Dipartimento di Automatica e Informatica, Turin, Italy

Pirrera, Simone ; Politecnico di Torino, Dipartimento di Automatica e Informatica, Turin, Italy

Regruto, Diego ; Politecnico di Torino, Dipartimento di Automatica e Informatica, Turin, Italy

External co-authors :

yes

Language :

English

Title :

A Non-Iterative Approach to Direct Data-Driven Control Design of MIMO LTI Systems

Publication date :

2023

Journal title :

IEEE Access

ISSN :

2169-3536

Publisher :

Institute of Electrical and Electronics Engineers Inc.

Volume :

Pages :

121671 - 121687

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

http://xplorestaging.ieee.org/ielx7/6287639/10005208/10304124.pdf?arnumber=10304124

Funders :

EU Framework Program for Research and Innovation within Horizon Europe—Marie Sklodowska-Curie Postdoctoral Fellowships through the BALSAM Project, in 2021

Available on ORBilu :

since 15 January 2026

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Bibliography

K. Astrom, ‘‘Direct methods for nonminimum phase systems,’’ in Proc. 19th IEEE Conf. Decis. Control Including Symp. Adapt. Processes, vol. 19, Dec. 1980, pp. 611–615.
A. S. Bazanella, M. Gevers, L. Mišković, and B. D. O. Anderson, ‘‘Iterative minimization of H2 control performance criteria,’’ Automatica, vol. 44, no. 10, pp. 2549–2559, Oct. 2008.
L. Campestrini, D. Eckhard, L. A. Chía, and E. Boeira, ‘‘Unbiased MIMO VRFT with application to process control,’’ J. Process Control, vol. 39, pp. 35–49, Mar. 2016.
L. Campestrini, D. Eckhard, M. Gevers, and A. S. Bazanella, ‘‘Virtual reference feedback tuning for non-minimum phase plants,’’ Automatica, vol. 47, no. 8, pp. 1778–1784, Aug. 2011.
M. C. Campi, A. Lecchini, and S. M. Savaresi, ‘‘Virtual reference feedback tuning: A direct method for the design of feedback controllers,’’ Automatica, vol. 38, no. 8, pp. 1337–1346, Aug. 2002.
M. C. Campi, A. Lecchini, and S. M. Savaresi, ‘‘An application of the virtual reference feedback tuning method to a benchmark problem,’’ Eur. J. Control, vol. 9, no. 1, pp. 66–76, Jan. 2003.
V. Cerone, D. Piga, and D. Regruto, ‘‘Improved parameter bounds for set-membership EIV problems,’’ Int. J. Adapt. Control Signal Process., vol. 25, no. 3, pp. 208–227, Mar. 2011.
V. Cerone, D. Piga, and D. Regruto, ‘‘Bounded error identification of Hammerstein systems through sparse polynomial optimization,’’ Automatica, vol. 48, no. 10, pp. 2693–2698, Oct. 2012.
V. Cerone, D. Piga, and D. Regruto, ‘‘Set-membership error-in-variables identification through convex relaxation techniques,’’ IEEE Trans. Autom. Control, vol. 57, no. 2, pp. 517–522, Feb. 2012.
V. Cerone, D. Piga, and D. Regruto, ‘‘Bounding the parameters of block-structured nonlinear feedback systems,’’ Int. J. Robust Nonlinear Control, vol. 23, no. 1, pp. 33–47, Jan. 2013.
V. Cerone, V. Razza, and D. Regruto, ‘‘Set-membership errors-in-variables identification of MIMO linear systems,’’ Automatica, vol. 90, pp. 25–37, Apr. 2018.
V. Cerone, D. Regruto, and M. Abuabiah, ‘‘Direct data-driven control design through set-membership errors-in-variables identification techniques,’’ in Proc. Amer. Control Conf. (ACC), May 2017, pp. 388–393.
V. Cerone, D. Regruto, and M. Abuabiah, ‘‘A set-membership approach to direct data-driven control design for SISO non-minimum phase plants,’’ in Proc. IEEE 56th Annu. Conf. Decis. Control (CDC), Dec. 2017, pp. 1284–1290.
V. Cerone, M. Abuabiah, and D. Regruto, ‘‘An H∞ method to design the reference model in direct data-driven control design,’’ in Proc. 59th IEEE Conf. Decis. Control (CDC), Dec. 2020, pp. 6004–6009.
G. Chesi, A. Garulli, A. Tesi, and A. Vicino, ‘‘Solving quadratic distance problems: An LMI-based approach,’’ IEEE Trans. Autom. Control, vol. 48, no. 2, pp. 200–212, Feb. 2003.
G. R. G. D. Silva, L. Campestrini, and A. S. Bazanella, ‘‘Multivariable VRFT: An approach for systems with non-minimum phase transmission zeros,’’ in Proc. IEEE Conf. Control Appl. (CCA), Sep. 2016, pp. 1324–1329.
G. R. G. D. Silva, L. Campestrini, and A. S. Bazanella, ‘‘Multivariable virtual reference feedback tuning for non-minimum phase plants,’’ IEEE Control Syst. Lett., vol. 2, no. 1, pp. 121–126, Jan. 2018.
S. Formentin, A. Bisoffi, and T. Oomen, ‘‘Asymptotically exact direct data-driven multivariable controller tuning,’’ IFAC-PapersOnLine, vol. 48, no. 28, pp. 1349–1354, 2015.
S. Formentin, S. M. Savaresi, and L. D. Re, ‘‘Non-iterative direct data-driven controller tuning for multivariable systems: Theory and application,’’ IET Control Theory Appl., vol. 6, no. 9, pp. 1250–1257, Jun. 2012.
G. R. G. D. Silva, A. S. Bazanella, and L. Campestrini, ‘‘One-shot data-driven controller certification,’’ ISA Trans., vol. 99, pp. 361–373, Apr. 2020.
K. Havre, ‘‘Effect of RHP zeros and poles on performance in multivariable systems,’’ in Proc. UKACC Int. Conf. Control. Control, vol. 2, 1996, pp. 930–935.
H. Hjalmarsson, ‘‘Efficient tuning of linear multivariable controllers using iterative feedback tuning,’’ Int. J. Adapt. Control Signal Process., vol. 13, no. 7, pp. 553–572, Nov. 1999.
H. Hjalmarsson, S. Gunnarsson, and M. Gevers, ‘‘A convergent iterative restricted complexity control design scheme,’’ in Proc. 33rd IEEE Conf. Decis. Control, vol. 2, Dec. 1994, pp. 1735–1740.
Z.-S. Hou and Z. Wang, ‘‘From model-based control to data-driven control: Survey, classification and perspective,’’ Inf. Sci., vol. 235, pp. 3–35, Jun. 2013.
A. Karimi, L. Mišković, and D. Bonvin, ‘‘Iterative correlation-based controller tuning,’’ Int. J. Adapt. Control Signal Process., vol. 18, no. 8, pp. 645–664, 2004.
A. Karimi, K. van Heusden, and D. Bonvin, ‘‘Non-iterative data-driven controller tuning using the correlation approach,’’ in Proc. Eur. Control Conf. (ECC), Jul. 2007, pp. 5189–5195.
A. Khan, W. Xie, L. Zhang, and L. Liu, ‘‘Design and applications of interval observers for uncertain dynamical systems,’’ IET Circuits, Devices Syst., vol. 14, no. 6, pp. 721–740, Sep. 2020.
A. Khan, W. Xie, B. Zhang, and L.-W. Liu, ‘‘A survey of interval observers design methods and implementation for uncertain systems,’’ J. Franklin Inst., vol. 358, no. 6, pp. 3077–3126, Apr. 2021.
J. B. Lasserre, ‘‘Global optimization with polynomials and the problem of moments,’’ SIAM J. Optim., vol. 11, no. 3, pp. 796–817, Jan. 2001.
J. B. Lasserre, Moments, Positive Polynomials and Their Applications, vol. 1. Singapore: World Scientific, 2009.
K. Latawiec, S. Bańka, and J. Tokarzewski, ‘‘Control zeros and nonminimum phase LTI MIMO systems,’’ Annu. Rev. Control, vol. 24, no. 1, pp. 105–112, 2000.
A. Lecchini and M. Gevers, ‘‘On iterative feedback tuning for nonminimum phase plants,’’ in Proc. 41st IEEE Conf. Decis. Control, vol. 4, Dec. 2002, pp. 4658–4663.
A. MacFarlane and N. Karcanias, ‘‘Poles and zeros of linear multivariable systems: A survey of the algebraic, geometric and complex-variable theory,’’ Int. J. Control, vol. 24, no. 1, pp. 33–74, 1976.
L. Mišković, A. Karimi, D. Bonvin, and M. Gevers, ‘‘Correlation-based tuning of decoupling multivariable controllers,’’ Automatica, vol. 43, no. 9, pp. 1481–1494, Sep. 2007.
P. A. Parrilo, ‘‘Semidefinite programming relaxations for semialgebraic problems,’’ Math. Program., vol. 96, no. 2, pp. 293–320, May 2003.
A. Patete, K. Furuta, and M. Tomizuka, ‘‘Self-tuning control based on generalized minimum variance criterion for auto-regressive models,’’ Automatica, vol. 44, no. 8, pp. 1970–1975, Aug. 2008.
G. Rallo, S. Formentin, and S. M. Savaresi, ‘‘On data-driven control design for non-minimum-phase plants: A comparative view,’’ in Proc. IEEE 55th Conf. Decis. Control (CDC), Dec. 2016, pp. 7159–7164.
A. Sala and A. Esparza, ‘‘Extensions to ‘virtual reference feedback tuning: A direct method for the design of feedback controllers,’’’ Automatica, vol. 41, no. 8, pp. 1473–1476, Aug. 2005.
S. Skogestad and I. Postlethwaite, Multivariable Feedback Control: Analysis and Design, vol. 2. New York, NY, USA: Wiley, 2007.
M. Tomizuka, ‘‘Zero phase error tracking algorithm for digital control,’’ J. Dyn. Syst., Meas., Control, vol. 109, no. 1, pp. 65–68, Mar. 1987.
E. Trulsson and L. Ljung, ‘‘Direct minimization methods for adaptive control of non-minimum phase systems,’’ IFAC Proc. Volumes, vol. 15, no. 4, pp. 631–635, Jun. 1982.
K. van Heusden, A. Karimi, and D. Bonvin, ‘‘Data-driven model reference control with asymptotically guaranteed stability,’’ Int. J. Adapt. Control Signal Process., vol. 25, no. 4, pp. 331–351, Apr. 2011.
K. van Heusden, A. Karimi, and T. Söderström, ‘‘On identification methods for direct data-driven controller tuning,’’ Int. J. Adapt. Control Signal Process., vol. 25, no. 5, pp. 448–465, May 2011.
Q.-G. Wang, Decoupling Control, vol. 285. Berlin, Germany: Springer, 2002.
P. Yan, D. Liu, D. Wang, and H. Ma, ‘‘Data-driven controller design for general MIMO nonlinear systems via virtual reference feedback tuning and neural networks,’’ Neurocomputing, vol. 171, pp. 815–825, Jan. 2016.
K. Yubai, H. Usami, and J. Hirai, ‘‘Correlation-based direct tuning of MIMO controllers by least-squares and its application to tension-and-speed control apparatus,’’ in Proc. ICCAS-SICE, Aug. 2009, pp. 931–936.