Research Papers

Multivariable Nonlinear Data-Driven Control With Application to Autonomous Vehicle Lateral Dynamics

[+] Author and Article Information
Olga Galluppi

Dipartimento di Elettronica,
Informazione e Bioingegneria,
Politecnico di Milano,
P.za L. Da Vinci 32,
Milano 20133, Italy
e-mail: olga.galluppi@polimi.it

Simone Formentin

Dipartimento di Elettronica,
Informazione e Bioingegneria,
Politecnico di Milano,
P.za L. Da Vinci 32,
Milano 20133, Italy
e-mail: simone.formentin@polimi.it

Sergio M. Savaresi

Dipartimento di Elettronica,
Informazione e Bioingegneria,
Politecnico di Milano,
P.za L. Da Vinci 32,
Milano 20133, Italy
e-mail: sergio.savaresi@polimi.it

Carlo Novara

Dipartimento di Elettronica e Telecomunicazioni,
Politecnico di Torino,
Corso Duca degli Abruzzi, 24,
Torino 10129, Italy
e-mail: carlo.novara@polito.it

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received May 31, 2018; final manuscript received May 23, 2019; published online June 27, 2019. Editor: Joseph Beaman.

J. Dyn. Sys., Meas., Control 141(10), 101012 (Jun 27, 2019) (12 pages) Paper No: DS-18-1262; doi: 10.1115/1.4043926 History: Received May 31, 2018; Revised May 23, 2019

Complex engineering systems are usually described by the interaction of several agents and characterized by highly nonlinear dynamics. Control of multivariable nonlinear systems is a widely explored topic, and many different studies have been presented in the scientific literature. However, most of the existing methods strongly rely upon an accurate model of the system, which is generally costly and/or hard to undertake in practice. In this work, we propose a multivariable extension of the data-driven inversion-based control (D2-IBC) method, where a model of the system is derived from data and considered relevant or not, based only on its weight on the final control performance. This method will prove its effectiveness on a challenging application: the stability control of a four-wheel steering autonomous vehicle.

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Khalil, H. , 1996, Nonlinear Systems, Prentice Hall, Upper Saddle River, NJ.
Hjalmarsson, H. , Gevers, M. , Gunnarsson, S. , and Lequin, O. , 1998, “ Iterative Feedback Tuning: Theory and Applications,” IEEE Control Syst., 18(4), pp. 26–41. [CrossRef]
Campi, M. C. , Lecchini, A. , and Savaresi, S. M. , 2002, “ Virtual Reference Feedback Tuning: A Direct Method for the Design of Feedback Controllers,” Automatica, 38(8), pp. 1337–1346. [CrossRef]
Safonov, M. G. , and Tsao, T.-C. , 1994, “ The Unfalsified Control Concept and Learning,” 33rd IEEE Conference on Decision and Control (CDC), Lake Buena Vista, FL, Dec. 14–16, pp. 2819–2824.
Campi, M. C. , and Savaresi, S. M. , 2006, “ Direct Nonlinear Control Design: The Virtual Reference Feedback Tuning (VRFT) Approach,” IEEE Trans. Autom. Control, 51(1), pp. 14–27. [CrossRef]
Novara, C. , Fagiano, L. , and Milanese, M. , 2013, “ Direct Feedback Control Design for Nonlinear Systems,” Automatica, 49(4), pp. 849–860. [CrossRef]
Novara, C. , Formentin, S. , Savaresi, S. M. , and Milanese, M. , 2016, “ Data-Driven Design of Two Degree-of-Freedom Nonlinear Controllers: The D2-IBC Approach,” Automatica, 72, pp. 19–27. [CrossRef]
Hou, Z.-S. , and Wang, Z. , 2013, “ From Model-Based Control to Data-Driven Control: Survey, Classification and Perspective,” Inf. Sci., 235, pp. 3–35. [CrossRef]
Tseng, H. E. , Ashrafi, B. , Madau, D. , Brown, T. A. , and Recker, D. , 1999, “ The Development of Vehicle Stability Control at Ford,” IEEE/ASME Trans. Mechatronics, 4(3), pp. 223–234. [CrossRef]
Huang, J. , and Tomizuka, M. , 2005, “ LTV Controller Design for Vehicle Lateral Control Under Fault in Rear Sensors,” IEEE/ASME Trans. Mechatronics, 10(1), pp. 1–7. [CrossRef]
Cho, W. , Choi, J. , Kim, C. , Choi, S. , and Yi, K. , 2012, “ Unified Chassis Control for the Improvement of Agility, Maneuverability, and Lateral Stability,” IEEE Trans. Veh. Technol., 61(3), pp. 1008–1020. [CrossRef]
Doumiati, M. , Victorino, A. C. , Charara, A. , and Lechner, D. , 2011, “ Onboard Real-Time Estimation of Vehicle Lateral Tire–Road Forces and Sideslip Angle,” IEEE/ASME Trans. Mechatronics, 16(4), pp. 601–614. [CrossRef]
Zhang, H. , and Wang, J. , 2016, “ Vehicle Lateral Dynamics Control Through AFS/DYC and Robust Gain-Scheduling Approach,” IEEE Trans. Veh. Technol., 65(1), pp. 489–494. [CrossRef]
Liebemann, E. , Meder, K. , Schuh, J. , and Nenninger, G. , 2004, “ Safety and Performance Enhancement: The Bosch Electronic Stability Control (ESP),” SAE Paper No. 2004-21–0060 https://www.sae.org/publications/technical-papers/content/2004-21-0060/.
Matthaeia, R. , Reschkaa, A. , Riekena, J. , Dierkesa, F. , Ulbricha, S. , Winkleb, T. , and Maurera, M. , 2015, Autonomous Driving: Technical, Legal and Social Aspects, Springer, Berlin.
Heißing, B. , and Ersoy, M. , 2010, Chassis Handbook: Fundamentals, Driving Dynamics, Components, Mechatronics, Perspectives, Springer Science and Business Media, Berlin.
Falcone, P. , Borrelli, F. , Asgari, J. , Tseng, H. E. , and Hrovat, D. , 2007, “ Predictive Active Steering Control for Autonomous Vehicle Systems,” IEEE Trans. Control Syst. Technol., 15(3), pp. 566–580. [CrossRef]
Ackermann, J. , Walter, W. , and Bünte, T. , 2004, “ Automatic Car Steering Using Robust Unilateral Decoupling,” International Conference on Advances in Vehicle Control and Safety. https://core.ac.uk/download/pdf/11097092.pdf
Pacejka, H. B. , Bakker, E. , and Nyborg, L. , 1987, “ Tyre Modelling for Use in Vehicle Dynamics Studies,” SAE Paper No. 870421.
Formentin, S. , Savaresi, S. M. , and del Re, L. , 2012, “ Non-Iterative Direct Data-Driven Controller Tuning for Multivariable Systems: Theory and Application,” IET Control Theory Appl., 6(9), pp. 1250–1257. [CrossRef]
Novara, C. , and Formentin, S. , 2018, “ Data-Driven Inversion-Based Control of Nonlinear Systems With Guaranteed Closed-Loop Stability,” IEEE Trans. Autom. Control, 63(4), pp. 1147–1154. [CrossRef]
Novara, C. , and Milanese, M. , 2014, “ Control of Nonlinear Systems: A Model Inversion Approach,” preprint arXiv:1407.1069.
Milanese, M. , and Novara, C. , 2007, “ Computation of Local Radius of Information in SM-IBC Identification of Nonlinear Systems,” J. Complexity, 23(4–6), pp. 937–951. [CrossRef]
Sjöberg, J. , Zhang, Q. , Ljung, L. , Benveniste, A. , Delyon, B. , Glorennec, P.-Y. , Hjalmarsson, H. , and Juditsky, A. , 1995, “ Nonlinear Black-Box Modeling in System Identification: A Unified Overview,” Automatica, 31(12), pp. 1691–1724. [CrossRef]
Novara, C. , Vincent, T. , Hsu, K. , Milanese, M. , and Poolla, K. , 2011, “ Parametric Identification of Structured Nonlinear Systems,” Automatica, 47(4), pp. 711–721. [CrossRef]
Tibshirani, R. , 1996, “ Regression Shrinkage and Selection Via the Lasso,” J. R. Stat. Soc. Ser. B (Methodol.), 58(1), pp. 267–288.
Formentin, S. , Novara, C. , Savaresi, S. M. , and Milanese, M. , 2015, “ Active Braking Control System Design: The D2-IBC Approach,” IEEE/ASME Trans. Mechatronics, 20(4), pp. 1573–1584. [CrossRef]
Kennedy, J. , 2010, “ Particle Swarm Optimization,” Encyclopedia of Machine Learning, Springer, Boston, MA, pp. 760–766.
Eberhart, R. C. , and Shi, Y. , 1998, “ Comparison Between Genetic Algorithms and Particle Swarm Optimization,” Evolutionary Programming VII, Springer, San Diego, CA, pp. 611–616.
Stoica, P. , and Jansson, M. , 2000, “ MIMO System Identification: State-Space and Subspace Approximations Versus Transfer Function and Instrumental Variables,” IEEE Trans. Signal Process., 48(11), pp. 3087–3099. [CrossRef]
Novara, C. , and Formentin, S. , 2018, “ Data-Driven Inversion-Based Control: Closed-Loop Stability Analysis for MIMO Systems,” preprint arXiv(2144372).
Nishio, A. , Tozu, K. , Yamaguchi, H. , Asano, K. , and Amano, Y. , 2001, “ Development of Vehicle Stability Control System Based on Vehicle Sideslip Angle Estimation,” SAE Paper No. 2001-01-0137.
Piyabongkarn, D. , Rajamani, R. , Grogg, J. A. , and Lew, J. Y. , 2009, “ Development and Experimental Evaluation of a Slip Angle Estimator for Vehicle Stability Control,” IEEE Trans. Control Syst. Technol., 17(1), pp. 78–88. [CrossRef]
Lgarias, J. C. , Reeds, J. A. , Wright, M. , and Wright, P. E. , 1998, “ Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions,” SIAM J. Optim., 9(1), pp. 112–147. [CrossRef]
Caruntu, C. F. , Lazar, M. , Gielen, R. H. , van den Bosch, P. , and Di Cairano, S. , 2013, “ Lyapunov Based Predictive Control of Vehicle Drivetrains Over Can,” Control Eng. Pract., 21(12), pp. 1884–1898. [CrossRef]


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Fig. 1

The system architecture to control

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Fig. 2

The D2-IBC control scheme

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Fig. 3

The virtual loop concept

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Fig. 4

The virtual loop applied to the D2-IBC scheme

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Fig. 5

The vehicle used in the simulation tests

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Fig. 6

η: A tradeoff choice between sparsity and accuracy

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Fig. 7

Priority factors ζ: a sensitivity study

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Fig. 8

MIMO D2-IBC scheme for the proposed application

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Fig. 10

Tracking performance in nominal conditions on the validation track

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Fig. 11

Tracking performance in nominal conditions on the validation track (detail)

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Fig. 12

Computational time Monte Carlo simulation for the two optimization routines

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Fig. 13

The single-track model

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Fig. 14

Tracking performance: a comparison between D2-IBC and MPC

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Fig. 15

Control action: a comparison between D2-IBC and MPC



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