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Integral MRAC with minimal controller synthesis and bounded adaptive gains: the continuous-time case. (English) Zbl 1349.93223
Summary: Model reference adaptive controllers designed via the Minimal Control Synthesis (MCS) approach are a viable solution to control plants affected by parameter uncertainty, unmodelled dynamics, and disturbances. Despite its effectiveness to impose the required reference dynamics, an apparent drift of the adaptive gains, which can eventually lead to closed-loop instability or alter tracking performance, may occasionally be induced by external disturbances. This problem has been recently addressed for this class of adaptive algorithms in the discrete-time case and for square-integrable perturbations by using a parameter projection strategy [the authors, “Discrete-time integral MRAC with minimal controller synthesis and parameter projection”, ibid. 352, No. 12, 5415–5436, (2015; doi:10.1016/j.jfranklin.2015.09.004)]. In this paper we tackle systematically this issue for MCS continuous-time adaptive systems with integral action by enhancing the adaptive mechanism not only with a parameter projection method, but also embedding a \(\sigma\)-modification strategy. The former is used to preserve convergence to zero of the tracking error when the disturbance is bounded and \(L_2\), while the latter guarantees global uniform ultimate boundedness under continuous \(L_\infty\) disturbances. In both cases, the proposed control schemes ensure boundedness of all the closed-loop signals. The strategies are numerically validated by considering systems subject to different kinds of disturbances. In addition, an electrical power circuit is used to show the applicability of the algorithms to engineering problems requiring a precise tracking of a reference profile over a long time range despite disturbances, unmodelled dynamics, and parameter uncertainty.

MSC:
93C40 Adaptive control/observation systems
93C41 Control/observation systems with incomplete information
93C73 Perturbations in control/observation systems
93B50 Synthesis problems
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[1] Montanaro, U.; Olm, J. M., Discrete-time integral MRAC with minimal controller synthesis and parameter projection, J. Frankl. Inst., 352, 12, 5415-5436, (2015) · Zbl 1395.93304
[2] Tao, G., Adaptive control design and analysis, (2003), John Wiley & Sons, Inc. Hoboken, NJ · Zbl 1061.93004
[3] Yang, Y.; Chen, X.; Li, C., Transient performance improvement in model reference adaptive control using image optimal method, J. Frankl. Inst., 352, 1, 16-32, (2015) · Zbl 1307.93212
[4] Ashok, R.; Shtessel, Y., Control of fuel cell-based electric power system using adaptive sliding mode control and observation techniques, J. Frankl. Inst., 352, 11, 4911-4934, (2015) · Zbl 1395.93139
[5] Yang, Y.; Ge, C.; Wang, H.; Li, X.; Hua, C., Adaptive neural network based prescribed performance control for teleoperation system under input saturation, J. Frankl. Inst., 352, 5, 1850-1866, (2015) · Zbl 1395.93315
[6] Chi, R.; Hou, Z.; Jin, S., A data-driven adaptive ILC for a class of nonlinear discrete-time systems with random initial states and iteration-varying target trajectory, J. Frankl. Inst., 352, 6, 2407-2424, (2015) · Zbl 1395.93292
[7] Li, Y.; Tong, S.; Li, T., Adaptive fuzzy output feedback dynamic surface control of interconnected nonlinear pure-feedback systems, IEEE Trans. Cybern., 45, 1, 138-149, (2015)
[8] Li, Y.; Tong, S.; Li, T., Composite adaptive fuzzy output feedback control design for uncertain nonlinear strict-feedback systems with input saturation, IEEE Trans. Cybern., 45, 10, 2299-2308, (2015)
[9] Y. Li, S. Tong, Adaptive fuzzy output-feedback stabilization control for a class of switched non-strict-feedback nonlinear systems, IEEE Trans. Cybern. (2016), in press, 10.1109/TCYB.2016.2536628.
[10] Stoten, D.; Benchoubane, H., Empirical studies of an MRAC algorithm with minimal controller synthesis, Int. J. Control, 51, 4, 823-849, (1990) · Zbl 0709.93043
[11] Stoten, D.; Benchoubane, H., Robustness of minimal controller synthesis algorithm, Int. J. Control, 51, 4, 851-861, (1990) · Zbl 0716.93026
[12] di Bernardo, M.; di Gaeta, A.; Montanaro, U.; Santini, S., Synthesis and experimental validation of the novel LQ-NEMCSI adaptive strategy on an electronic throttle valve, IEEE Trans. Control Syst. Technol., 18, 6, 1325-1337, (2010)
[13] M. di Bernardo, A. di Gaeta, U. Montanaro, J. Olm, S. Santini, Discrete-time MRAC with Minimal Controller Synthesis of an electronic throttle body, in: Proceedings of 18th IFAC World Congress, 2011, pp. 5064-5069.
[14] Montanaro, U.; di Gaeta, A.; Giglio, V., Adaptive tracking control of a common rail injection system for gasoline enginesa discrete-time integral minimal control synthesis approach, IEEE Trans. Control Syst. Technol., 21, 5, 1940-1948, (2013)
[15] U. Montanaro, A. di Gaeta, V. Giglio, An MRAC approach for tracking and ripple attenuation of the common rail pressure for GDI engines, in: Proceedings of 18th IFAC World Congress, 2011, pp. 4173-4180.
[16] di Gaeta, A.; Hoyos-Velasco, C.; Montanaro, U., Cycle-by-cycle adaptive force compensation for the soft-landing control of an electro-mechanical engine valve actuator, Asian J. Control, 17, 5, 1707-1724, (2015) · Zbl 1333.93151
[17] Stoten, D.; di Bernardo, M., Application of the minimal control synthesis algorithm to the control and synchronization of chaotic systems, Int. J. Control, 65, 6, 925-938, (1996) · Zbl 0867.93073
[18] Stoten, D.; Gómez, E., Adaptive control of shaking tables using the minimal controller synthesis algorithm, Philos. Trans. R. Soc. Lond., 357, 9, 1697-1723, (2001) · Zbl 1049.93549
[19] Hillis, A.; Harrison, A.; Stoten, D., A comparison of two adaptive algorithms for the control of active engine mounts, J. Sound Vib., 286, 1-2, 37-54, (2005)
[20] A. Gizatullin, K. Edge, Adaptive control for a multi-axis hydraulic test rig, Proc. Inst. Mech. Eng. - Part I: J. Syst. Control Eng. 221 (2) (2007) 183-198.
[21] L. Rossi, A. Irace, U. Montanaro, M. di Bernardo, G. Breglio, Structural vibration control of a cantilever beam by MRAC method, in: Proceedings of 2nd International Symposium on Reliability of Optoelectronics For Space, Cagliari, Italy, 2010.
[22] Benchoubane, H.; Stoten, D., The decentralized minimal controller synthesis algorithm, Int. J. Control, 56, 4, 967-983, (1992) · Zbl 0761.93019
[23] Stoten, D.; Benchoubane, H., The extended minimal controller synthesis algorithm, Int. J. Control, 56, 5, 1139-1165, (1992) · Zbl 0777.93025
[24] D. Stoten, S. Neild, The error-based minimal control synthesis algorithm with integral action, Proc. Inst. Mech. Eng. - Part I: J. Syst. Control Eng. 217 (3) (2003) 187-201.
[25] di Bernardo, M.; Montanaro, U.; Santini, S., Minimal control synthesis adaptive control of continuous bimodal piecewise affine systems, SIAM J. Control Optim., 48, 7, 4242-4261, (2010) · Zbl 1214.93046
[26] di Bernardo, M.; Montanaro, U.; Santini, S., Hybrid model reference adaptive control of piecewise affine systems, IEEE Trans. Autom. Control, 58, 2, 304-316, (2013) · Zbl 1369.93325
[27] di Bernardo, M.; Hoyos-Velasco, C.; Montanaro, U.; Santini, S., Experimental implementation and validation of a novel minimal control synthesis adaptive controller for continuous bimodal piecewise affine systems, Control Eng. Pract., 20, 3, 269-281, (2012)
[28] di Bernardo, M.; di Gennaro, F.; Olm, J. M.; Santini, S., Discrete-time minimal control synthesis adaptive algorithm, Int. J. Control, 83, 4, 2641-2657, (2010) · Zbl 1205.93098
[29] di Bernardo, M.; di Gaeta, A.; Montanaro, U.; Olm, J. M.; Santini, S., Experimental validation of the discrete-time MCS adaptive strategy, Control Eng. Pract., 21, 6, 847-859, (2013)
[30] di Bernardo, M.; Montanaro, U.; Olm, J.; Santini, S., Model reference adaptive control of discrete-time piecewise linear systems, Int. J. Robust Nonlinear Control, 23, 7, 709-730, (2013) · Zbl 1273.93100
[31] Montanaro, U.; di Gaeta, A.; Giglio, V., Robust discrete-time MRAC with minimal controller synthesis of an electronic throttle body, IEEE/ASME Trans. Mechatron., 19, 2, 524-537, (2014)
[32] B. Anderson, R. Bitmead, C. Johnson, P. Kokotovic, R. Kosut, I. Mareels, L. Praly, B. Riedle, Stability of Adaptive Systems: Passivity and Averaging Analysis, The M.I.T. Press, Cambridge, MA and London, 1986. · Zbl 0722.93036
[33] S. Sebusang, D. Stoten, Controller gain bounding in the minimal control synthesis algorithm, in: Proceedings of 30th Southeastern Symposium on System Theory, 1998, pp. 141-145.
[34] Khalil, H., Nonlinear systems, (2002), Prentice Hall, Upper Saddle River, NJ
[35] Mohan, N.; Undeland, T.; Robbins, W., Power electronics: converters, applications, and design, (2002), Cambridge University Press, New York
[36] Hodgson, S.; Stoten, D., Passivity-based analysis of the minimal control synthesis algorithm, Int. J. Control, 63, 1, 67-84, (1996) · Zbl 0854.93055
[37] D. Stoten, The adaptive minimal control synthesis algorithm with integral action, in: Proceedings of 21st International Conference on Industrial Electronics, Control, and Instrumentation, vol. 2, 1995, pp. 1646-1651.
[38] A. Salvi, S. Santini, D. Biel, J. Olm, M. di Bernardo, Model reference adaptive control of a full-bridge buck inverter with Minimal Controller synthesis, in: Proceedings of IEEE 52nd Conference on Decision and Control, 2012, pp. 3469-3474.
[39] S. Malo, R. Grinó, Adaptive feed-forward cancellation control of a full-bridge dc-ac voltage inverter, in: Proceedings of 17th IFAC World Congress, 2008, pp. 4571-4576.
[40] Bursi, O.; Stoten, D.; Vulcan, L., Convergence and frequency-domain analysis of a discrete first-order model reference adaptive controller, Struct. Control Health Monit., 14, 5, 777-807, (2007)
[41] di Bernardo, M.; Montanaro, U.; Ortega, R.; Santini, S., Extended hybrid model reference adaptive control of piecewise affine systems, Nonlinear Anal.: Hybrid Syst., 21, 11-21, (2016) · Zbl 1338.93205
[42] U. Montanaro, Model Reference Adaptive Control of Piecewise Affine Systems and Applications (Ph.D. dissertation), University of Naples Federico II, Faculty of Engineering, Naples, Italy, 2009.
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