Data-driven design of two degree-of-freedom nonlinear controllers: the \(\operatorname{D}^2\)-IBC approach. (English) Zbl 1344.93054
Summary: In this paper, we introduce and discuss the Data-Driven Inversion-Based Control (\(\operatorname{D}^2\)-IBC) method for nonlinear control system design. The method relies on a two degree-of-freedom architecture, with a nonlinear controller and a linear controller running in parallel, and does not require any detailed physical knowledge of the plant to control. Specifically, we use input/output data to synthesize the controller by employing convex optimization tools. We show the effectiveness of the proposed approach on a benchmark simulation example, regarding control of the Duffing system.
MSC:
| 93C10 | Nonlinear systems in control theory |
| 93B51 | Design techniques (robust design, computer-aided design, etc.) |
| 93B50 | Synthesis problems |
| 90C25 | Convex programming |
References:
| [1] | Campi, M. C.; Lecchini, A.; Savaresi, S. M., Virtual reference feedback tuning: a direct method for the design of feedback controllers, Automatica, 38, 8, 1337-1346 (2002) · Zbl 1008.93037 |
| [2] | Campi, M. C.; Savaresi, S. M., Direct nonlinear control design: The virtual reference feedback tuning (vrft) approach, IEEE Transactions on Automatic Control, 51, 1, 14-27 (2006) · Zbl 1366.93251 |
| [3] | Candes, E. J.; Romberg, J.; Tao, T., Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information, IEEE Transactions on Information Theory, 52, 2, 489-509 (2006) · Zbl 1231.94017 |
| [4] | Donoho, D. L.; Elad, M.; Temlyakov, V. N., Stable recovery of sparse overcomplete representations in the presence of noise, IEEE Transactions on Information Theory, 52, 1, 6-18 (2006) · Zbl 1288.94017 |
| [5] | Doyle, J.; Francis, B. A.; Tannenbaum, A., Feedback control theory (1992), Macmillan Publishing Company: Macmillan Publishing Company New York |
| [7] | (Findeisen, R.; Allgower, F.; Biegel, L. T., Assessment and future directions of nonlinear model predictive control. Assessment and future directions of nonlinear model predictive control, Lecture notes in control and information sciences (2007), Springer) · Zbl 1116.93009 |
| [8] | Formentin, S.; Corno, M.; Savaresi, S. M.; Del Re, L., Direct data-driven control of linear time-delay systems, Asian Journal of Control, 14, 3, 652-663 (2012) · Zbl 1303.93086 |
| [9] | Formentin, S.; De Filippi, P.; Corno, M.; Tanelli, M.; Savaresi, S. M., Data-driven design of braking control systems, IEEE Transactions on Control Systems Technology, 21, 1, 186-193 (2013) |
| [11] | Formentin, S.; Karimi, A., A data-driven approach to mixed-sensitivity control with application to an active suspension system, IEEE Transactions on Industrial Informatics, 9, 4, 2293-2300 (2013) |
| [12] | Formentin, S.; Karimi, A., Enhancing statistical performance of data-driven controller tuning via l2-regularization, Automatica, 50, 5, 1514-1520 (2014) · Zbl 1296.93062 |
| [13] | Formentin, S.; Karimi, A.; Savaresi, S. M., Optimal input design for direct data-driven tuning of model-reference controllers, Automatica, 49, 6, 1874-1882 (2013) · Zbl 1360.93722 |
| [14] | Formentin, S.; Savaresi, S. M.; Del Re, L., Non-iterative direct data-driven controller tuning for multivariable systems: theory and application, IET Control Theory & Applications, 6, 9, 1250-1257 (2012) |
| [15] | Fuchs, J. J., Recovery of exact sparse representations in the presence of bounded noise, IEEE Transactions on Information Theory, 51, 10, 3601-3608 (2005) · Zbl 1286.94031 |
| [16] | Gevers, M., Connecting identification and robust control, (The modeling of uncertainty in control systems (1994), Springer), 35-37 |
| [17] | Gevers, M., Identification for control: From the early achievements to the revival of experiment design, European Journal of Control, 11, 4, 335-352 (2005) · Zbl 1293.93206 |
| [18] | (Grune, L.; Pannek, J., Nonlinear model predictive control—theory and algorithms. Nonlinear model predictive control—theory and algorithms, Communications and control engineering (2011), Springer) · Zbl 1220.93001 |
| [19] | Guardabassi, G.; Savaresi, S. M., Approximate linearization via feedback—an overview, Automatica, 37, 1, 1-15 (2001) · Zbl 0963.93002 |
| [20] | Hagenmeyer, V.; Delaleau, E., Exact feedforward linearization based on differential flatness, International Journal of Control, 76, 6, 537-556 (2003) · Zbl 1071.93012 |
| [21] | Hjalmarsson, H.; Gevers, M.; De Bruyne, F., For model-based control design, closed-loop identification gives better performance, Automatica, 32, 12, 1659-1673 (1996) · Zbl 0874.93038 |
| [22] | Hsu, K.; Novara, C.; Vincent, T.; Milanese, M.; Poolla, K., Parametric and nonparametric curve fitting, Automatica, 42, 11, 1869-1873 (2006) · Zbl 1120.65013 |
| [24] | Khalil, H. K., Nonlinear systems (1996), Prentice Hall |
| [25] | Ljung, L., System identification: theory for the user (1999), Prentice Hall: Prentice Hall Upper Saddle River, N.J |
| [26] | (Magni, L.; Raimondo, D. M.; Allgower, F., Nonlinear model predictive control—towards new challenging applications. Nonlinear model predictive control—towards new challenging applications, Lecture notes in control and information sciences (2009), Springer) · Zbl 1165.93004 |
| [27] | Marino, R.; Tomei, P., Nonlinear control design: geometric, adaptive and robust (1996), Prentice Hall International (UK) Ltd |
| [28] | Mayne, D. Q.; Rawlings, J. B.; Rao, C. V.; Scokaert, P. O.M., Constrained model predictive control: Stability and optimality, Automatica, 36, 6, 789-814 (2000) · Zbl 0949.93003 |
| [29] | Nijmeijer, H.; Savaresi, S. M., On approximate model-reference control of siso discrete-time nonlinear systems, Automatica, 34, 10, 1261-1266 (1998) · Zbl 0949.93037 |
| [30] | Novara, C., Sparse identification of nonlinear functions and parametric set membership optimality analysis, IEEE Transactions on Automatic Control, 57, 12, 3236-3241 (2012) · Zbl 1369.41030 |
| [31] | Novara, C.; Fagiano, L.; Milanese, M., Direct feedback control design for nonlinear systems, Automatica, 49, 4, 849-860 (2013) · Zbl 1285.93041 |
| [34] | Novara, C.; Vincent, T.; Hsu, K.; Milanese, M.; Poolla, K., Parametric identification of structured nonlinear systems, Automatica, 47, 4, 711-721 (2011) · Zbl 1215.93145 |
| [36] | Passenbrunner, T. E.; Formentin, S.; Savaresi, S. M.; Del Re, L., Direct multivariable controller tuning for internal combustion engine test benches, Control Engineering Practice, 29, 115-122 (2014) |
| [37] | Polycarpou, M. M., Stable adaptive neural control scheme for nonlinear systems, IEEE Transactions on Automatic Control, 41, 3, 447-451 (1996) · Zbl 0846.93060 |
| [38] | Radac, M. B.; Precup, R. E.; Petriu, E. M.; Preitl, S.; Dragos, C. A., Data-driven reference trajectory tracking algorithm and experimental validation, IEEE Transactions on Industrial Informatics, 9, 4, 2327-2336 (2013) |
| [39] | Ravi Sriniwas, G.; Arkun, Y., A global solution to the nonlinear model predictive control algorithms using polynomial arx models, Computers and Chemical Engineering, 21, 4, 431-439 (1997) |
| [40] | Savaresi, S. M.; Guardabassi, G. O., Approximate I/O feedback linearization of discrete-time non-linear systems via virtual input direct design, Automatica, 34, 6, 715-722 (1998) · Zbl 0945.93522 |
| [41] | Sjöberg, J.; Zhang, Q.; Ljung, L.; Benveniste, A.; Delyon, B.; Glorennec, P., Nonlinear black-box modeling in system identification: a unified overview, Automatica, 31, 1691-1723 (1995) · Zbl 0846.93018 |
| [42] | Tropp, J. A., Just relax: convex programming methods for identifying sparse signals in noise, IEEE Transactions on Information Theory, 52, 3, 1030-1051 (2006) · Zbl 1288.94025 |
| [43] | Yeşildirek, A.; Lewis, F. L., Feedback linearization using neural networks, Automatica, 31, 11, 1659-1664 (1995) · Zbl 0847.93032 |
| [44] | Ziegler, J. G.; Nichols, N. B., Optimum settings for automatic controllers, Transactions of the ASME, 64, 11 (1942) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
