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Adaptive tracking control for stochastic mechanical systems with actuator nonlinearities. (English) Zbl 1364.93750

Summary: In this paper, output tracking control problem is investigated for a class of uncertain nonlinear random mechanical systems subjected to unknown actuator nonlinearities. Two common kinds of actuator nonlinearities, namely, Bouc-Wen hysteresis and dead-zone, are considered in a unified framework, such that the designed adaptive control law is robust to the mentioned actuator nonlinearities (hysteresis and dead-zone). Different from some existing controller design approaches for nonlinear systems with actuator nonlinearities, the usual priori knowledge on the known compact set for system uncertain parameters has been eliminated with the proposed control method. The proposed control law can ensure that the system output tracking error eventually converges to an arbitrarily small neighborhood of zero in the sense of mean square by turning controller gains. Simulation studies are performed to demonstrate the effectiveness of the proposed controller design approach.

MSC:

93E03 Stochastic systems in control theory (general)
93C10 Nonlinear systems in control theory
70Q05 Control of mechanical systems
93C40 Adaptive control/observation systems
93B35 Sensitivity (robustness)
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[1] Yao, J.; Jiao, Z.; Ma, D.; Yan, L., High-accuracy tracking control of hydraulic rotary actuators with modeling uncertainties, IEEE/ASME Trans. Mechatron., 19, 2, 633-641 (2014)
[2] Zhang, L.; Wang, S.; Karimi, H. R.; Jasra, A., Robust finite-time control of switched linear systems and application to a class of servomechanism systems, IEEE/ASME Trans. Mechatron., 20, 5, 2476-2485 (2015)
[3] Yao, J.; Jiao, Z.; Ma, D., Extended-state-observer-based output feedback nonlinear robust control of hydraulic systems with backstepping, IEEE Trans. Ind. Electron., 61, 11, 6285-6293 (2014)
[4] Pan, H.; Sun, W.; Gao, H.; Yu, J., Finite-time stabilization for vehicle active suspension systems with hard constraints, IEEE Trans. Intell. Transp. Syst., 16, 5, 2663-2672 (2015)
[5] Wang, Y.; Li, F.-M.; Wang, Y.-Z., Nonlinear vibration of double layered viscoelastic nanoplates based on nonlocal theory, Physica E, 67, 65-76 (2015)
[6] Wang, Y.; Li, F.-M.; Wang, Y.-Z., Homoclinic behaviors and chaotic motions of double layered viscoelastic nanoplates based on nonlocal theory and extended Melnikov method, Chaos, 25, 6, 063108 (2015)
[7] Sun, W.; Tang, S.; Gao, H.; Zhao, J., Two time-scale tracking control of nonholonomic wheeled mobile robots, IEEE Trans. Control Syst. Technol., 24, 6, 2059-2069 (2016)
[8] Chen, Z.; Yao, B.; Wang, Q., Accurate motion control of linear motors with adaptive robust compensation of nonlinear electromagnetic field effect, IEEE/ASME Trans. Mechatron., 18, 3, 1122-1129 (2013)
[9] Sun, W.; Zhang, Y.; Huang, Y.; Gao, H.; Kaynak, O., Transient-performance-guaranteed robust adaptive control and its application to precision motion control systems, IEEE Trans. Ind. Electron., 63, 10, 6510-6518 (2016)
[10] Pan, H.; Sun, W.; Gao, H.; Jing, X., Disturbance observer-based adaptive tracking control with actuator saturation and its application, IEEE Trans. Autom. Sci. Eng., 13, 2, 868-875 (2015)
[11] Chen, Z.; Yao, B.; Wang, Q., \(μ\)-synthesis-based adaptive robust control of linear motor driven stages with high-frequency dynamics: a case study, IEEE/ASME Trans. Mechatron., 20, 3, 1482-1490 (2015)
[12] Pan, H.; Sun, W.; Gao, H.; Hayat, T.; Alsaadi, F., Nonlinear tracking control based on extended state observer for vehicle active suspensions with performance constraints, Mechatronics, 30, 363-370 (2015)
[13] Pan, H.; Sun, W.; Gao, H.; Kaynak, O.; Alsaadi, F.; Hayat, T., Robust adaptive control of non-linear time-delay systems with saturation constraints, IET Control Theory Appl., 9, 1, 103-113 (2015)
[14] Sun, W.; Pan, H.; Gao, H., Filter-based adaptive vibration control for active vehicle suspensions with electrohydraulic actuators, IEEE Trans. Veh. Technol., 65, 6, 4619-4626 (2016)
[15] Zhou, J.; Wen, C.; Li, T., Adaptive output feedback control of uncertain nonlinear systems with hysteresis nonlinearity, IEEE Trans. Autom. Control, 57, 10, 2627-2633 (2012) · Zbl 1369.93323
[16] Zhang, T.; Ge, S. S., Adaptive neural control of mimo nonlinear state time-varying delay systems with unknown dead-zones and gain signs, Automatica, 43, 6, 1021-1033 (2007) · Zbl 1282.93152
[17] Zhang, L.; Zhu, Y.; Shi, P.; Zhao, Y., Resilient asynchronous filtering for Markov jump neural networks with unideal measurements and multiplicative noises, IEEE Trans. Cybernet., 45, 12, 2840-2852 (2015)
[18] Yang, X.; Cao, X.; Gao, H., Sampled-data control for relative position holding of spacecraft rendezvous with thrust nonlinearity, IEEE Trans. Ind. Electron., 59, 2, 1146-1153 (2012)
[19] Yang, X.; Yin, S., Variational Bayesian inference for FIR models with randomly missing measurements, IEEE Trans. Ind. Electron. (2016)
[20] Feng, Z.; Zheng, W. X., On extended dissipativity of discrete-time neural networks with time delay, IEEE Trans. Neural Networks Learn. Syst., 26, 12, 3293-3300 (2015)
[21] Pan, H.; Jing, X.; Sun, W., Robust finite-time tracking control for nonlinear suspension systems via disturbance compensation, Mech. Syst. Signal Process., 88, 49-61 (2017)
[22] Zhang, L.; Leng, Y.; Colaneri, P., Stability and stabilization of discrete-time semi-Markov jump linear systems via semi-Markov kernel approach, IEEE Trans. Autom. Control, 61, 2, 503-508 (2016) · Zbl 1359.93524
[23] Feng, Z.; Zheng, W. X., On reachable set estimation of delay Markovian jump systems with partially known transition probabilities, J. Franklin Inst., 353, 15, 3835-3856 (2016) · Zbl 1347.93247
[24] Fei, Z.; Guan, C.; Shi, P., Further results on H control for discrete-time Markovian jump time-delay systems, Int. J. Control (2016), in press
[25] Deng, H.; Krstic, M.; Williams, R. J., Stabilization of stochastic nonlinear systems driven by noise of unknown covariance, IEEE Trans. Autom. Control, 46, 8, 1237-1253 (2001) · Zbl 1008.93068
[26] Krstic, M.; Modestino, J.; Deng, H.; Fettweis, A.; Massey, J.; Thoma, M.; Sontag, E.; Dickinson, B., Stabilization of Nonlinear Uncertain Systems (1998), Springer-Verlag, New York, Inc. · Zbl 0906.93001
[27] Kovaleva, A.; Akulenko, L., Approximation of escape time for Lagrangian systems with fast noise, IEEE Trans. Autom. Control, 52, 12, 2338-2341 (2007) · Zbl 1366.82043
[28] Cui, M. Y.; Wu, Z.-J.; Xie, X.-J.; Shi, P., Modeling and adaptive tracking for a class of stochastic Lagrangian control systems, Automatica, 49, 3, 770-779 (2013) · Zbl 1267.93161
[29] Constantinou, M. C.; Kneifati, M. C., Dynamics of soil-base-isolated-structure systems, J. Struct. Eng., 114, 1, 211-221 (1988)
[30] Ma, F.; Zhang, H.; Bockstedte, A.; Foliente, G. C.; Paevere, P., Parameter analysis of the differential model of hysteresis, J. Appl. Mech., 71, 3, 342-349 (2004) · Zbl 1111.74534
[31] Tong, S.; Wang, T.; Li, Y.; Zhang, H., Adaptive neural network output feedback control for stochastic nonlinear systems with unknown dead-zone and unmodeled dynamics, IEEE Trans. Cybernet., 44, 6, 910-921 (2014)
[32] Wong, E.; Zakai, M., Riemann-Stieltjes approximations of stochastic integrals, Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 12, 2, 87-97 (1969) · Zbl 0185.44401
[33] Tong, S.; Zhang, L.; Li, Y., Observed-based adaptive fuzzy decentralized tracking control for switched uncertain nonlinear large-scale systems with dead zones, IEEE Trans. Syst. Man Cybernet.: Syst., 46, 1, 37-47 (2016)
[34] Jayawardhana, B.; Weiss, G., Tracking and disturbance rejection for fully actuated mechanical systems, Automatica, 44, 11, 2863-2868 (2008) · Zbl 1152.93403
[35] Patre, P. M.; MacKunis, W.; Dupree, K.; Dixon, W. E., Modular adaptive control of uncertain Euler-Lagrange systems with additive disturbances, IEEE Trans. Autom. Control, 56, 1, 155-160 (2011) · Zbl 1368.93312
[36] Khalil, H. K.; Grizzle, J., Nonlinear Systems, vol. 3 (2002), Prentice Hall: Prentice Hall Upper Saddle River · Zbl 1003.34002
[37] Su, C. Y.; Stepanenko, Y.; Svoboda, J.; Leung, T.-P., Robust adaptive control of a class of nonlinear systems with unknown backlash-like hysteresis, IEEE Trans. Autom. Control, 45, 12, 2427-2432 (2000) · Zbl 0990.93118
[38] Zhou, J.; Wen, C.; Zhang, Y., Adaptive backstepping control of a class of uncertain nonlinear systems with unknown backlash-like hysteresis, IEEE Trans. Autom. Control, 49, 10, 1751-1759 (2004) · Zbl 1365.93251
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