×

Adaptive fuzzy control for full states constrained systems with nonstrict-feedback form and unknown nonlinear dead zone. (English) Zbl 1429.93208

Summary: This paper addresses the problem of direct adaptive fuzzy tracking control design for a class of uncertain nonstrict-feedback systems with nonlinear dead zone and full state constraints. Fuzzy logic systems are used to approximate some unknown nonlinear functions and less adjustable parameters are adopted in each backstepping design process. This advantage is first to take into account the full state constrained nonstrict-feedback systems with input dead zone nonlinearity. To guarantee that the full state constraints are not violated, a novel adaptive fuzzy controller is developed by introducing barrier Lyapunov function with the error variables. Furthermore, it is proved that all the closed-loop signals remain semi-globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin. Two simulation examples are provided to verify the effectiveness of the proposed control method.

MSC:

93C42 Fuzzy control/observation systems
93C40 Adaptive control/observation systems
93B52 Feedback control
Full Text: DOI

References:

[1] Arqub, O. A., Adaptation of reproducing kernel algorithm for solving fuzzy fredholm-volterra integrodifferential equations, Neural Comput. Appl. (2015)
[2] Arqub, O. A.; AL-Smadi, M.; Momani, S.; Hayat, T., Numerical solutions of fuzzy differential equations using reproducing kernel hilbert space method, Soft Comput. (2015)
[3] Chen, B.; Liu, X. P.; Liu, K.; Lin, C., Direct adaptive fuzzy control of nonlinear strict-feedback systems, Automatica., 45, 6, 1530-1535 (2009) · Zbl 1166.93341
[4] Chen, W.; Jiao, L.; Li, R.; Li, J., Adaptive backstepping fuzzy control for nonlinearly parameterized systems with periodic disturbances, IEEE Trans. Fuzzy Syst., 18, 4, 674-685 (2010)
[5] Chen, W.; Ge, S. S.; Wu, J.; Gong, M., Globally stable adaptive backstepping neural network control for uncertain strict-feedback systems with tracking accuracy known a priori, IEEE Trans. Neural Networks Learn.Syst., 26, 9, 1842-1854 (2015)
[6] Chen, B.; Liu, X. P.; Ge, S. S.; Lin, C., Adaptive fuzzy control of a class of nonlinear systems by fuzzy approximation approach, IEEE Trans. Fuzzy Syst.., 20, 6, 1012-1021 (2012)
[7] Chen, B.; Liu, X. P.; Liu, K. F.; Lin, C., Fuzzy approximation-based adaptive control of nonlinear delayed systems with unknown dead zone, IEEE Trans. Fuzzy Syst., 22, 2, 237-248 (2014)
[8] Chen, B.; Lin, C.; Liu, X. P.; Liu, K. F., Adaptive fuzzy tracking control for a class of MIMO nonlinear systems in nonstrict-feedback form, IEEE Trans. Cybern., 45, 12, 2744-2755 (2015)
[9] Chen, B.; Lin, C.; Liu, X. P.; Liu, K. F., Observer-based adaptive fuzzy control for a class of nonlinear delayed systems, IEEE Trans. Syst., Man Cybern., 46, 1, 27-36 (2016)
[10] Chen, M.; Ge, S. S.; Ren, B., Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints, Automatica., 47, 3, 452-465 (2011) · Zbl 1219.93053
[11] Chen, M.; Shi, P.; Lim, C. C., Adaptive neural fault-tolerant control of a 3-DOF model helicopter system, IEEE Trans. Syst., Man Cybern., 46, 2, 260-270 (2016)
[12] Hua, C. C.; Li, Y. F., Output feedback prescribed performance control for interconnected time-delay systems with unknown prandtl¿CIshlinskii hysteresis, J. Franklin Inst., 352, 7, 2750-2764 (2015) · Zbl 1395.93298
[13] Ho, J. K.; Geun, B. K.; Jin, B. P.; Young, H. J., Decentralized sampled-data \(H_∞\) fuzzy filter for nonlinear large-scale systems, Fuzzy Sets Syst., 273, 68-86 (2015) · Zbl 1373.93017
[14] He, W.; Ge, S. S.; How, B. V.E.; Choo, Y. S.; Hong, K. S., Robust adaptive boundary control of a flexible marine riser with vessel dynamics, Automatica., 47, 4, 722-732 (2011) · Zbl 1215.93073
[15] He, W.; Zhang, S.; Ge, S. S., Adaptive control of a flexible crane system with the boundary output constraint, IEEE Trans. Ind. Electron., 61, 8, 4126-4133 (2014)
[16] He, W.; Zhang, S.; Ge, S. S., Robust adaptive control of a thruster assisted position mooring system, Automatica., 50, 7, 1843-1851 (2014) · Zbl 1296.93084
[17] Jiang, Y.; Yang, C.; Ma, H., A review of fuzzy logic and neural network based intelligent control design for discrete-time systems, Discrete Dyn. Nat. and Soc. (2016) · Zbl 1417.93191
[18] Yoo, S. J., Adaptive neural tracking and obstacle avoidance of uncertain mobile robots with unknown skidding and slipping, Inf. Sci., 238, 176-189 (2013) · Zbl 1321.93050
[19] Kim, B. S.; Yoo, S. J., Approximation-based adaptive control of uncertain non-linear pure-feedback systems with full state constraints, IET Control Theory Appl., 8, 17, 2070-2081 (2014)
[20] Krstic, M.; Kanellakopoulos, I.; Kokotovic, P. V., Nonlinear and Adaptive Control Design. (1995), Wiley-Interscience: Wiley-Interscience New York · Zbl 0763.93043
[21] Li, Z.; Yang, C.; Su, C.; Ye, W., Adaptive fuzzy-based motion generation and control of mobile under-actuated manipulators, Eng. Appl. Artif. Intell., 30, 86-95 (2014)
[22] Li, Y. M.; Tong, S. C.; Li, T. S., Observer-based adaptive fuzzy tracking control of MIMO stochastic nonlinear systems with unknown control directions and unknown dead zones, IEEE Trans. Fuzzy Syst., 23, 4, 1228-1241 (2015)
[23] Li, Y. M.; Tong, S. C.; Li, T. S., Adaptive fuzzy output feedback dynamic surface control of interconnected nonlinear pure-feedback systems, IEEE Trans. Cybern., 45, 1, 138-149 (2015)
[24] Liu, Y. J.; Tong, S. C., Adaptive fuzzy identification and control for a class of nonlinear pure-feedback MIMO systems with unknown dead-zones, IEEE Trans. Fuzzy Syst., 23, 5, 1387-1398 (2015)
[25] Liu, Y. J.; Tong, S. C., Adaptive fuzzy control for a class of unknown nonlinear dynamical systems, Fuzzy Sets Syst., 263, 49-70 (2015) · Zbl 1361.93024
[26] Liu, Y. J.; Tong, S. C., Adaptive fuzzy control for a class of nonlinear discrete-time systems with backlash, IEEE Trans. Fuzzy Syst., 22, 5, 1359-1365 (2014)
[27] Li, Y. M.; Tong, S. C., Adaptive fuzzy output-feedback stabilization control for a class of switched non-strict-feedback nonlinear systems, IEEE Trans.Cybern. (2016)
[28] Liu, Y. J.; Tong, S. C., Barrier lyapunov functions-based adaptive control for a class of nonlinear pure-feedback systems with full state constraints, Automatica., 64, 2, 70-75 (2016) · Zbl 1329.93088
[29] Liu, Z.; Chen, C.; Zhang, Y.; Chen, C. L.P., Coordinated fuzzy control of robotic arms with actuator nonlinearities and motion constraints, Inf. Sci., 296, 1-13 (2015) · Zbl 1360.93472
[30] Li, Y. X.; Yang, G. H., Robust adaptive fuzzy control of a class of uncertain switched nonlinear systems with mismatched uncertainties, Inf. Sci., 339, 290-309 (2016) · Zbl 1396.93083
[31] Li, Y. M.; Tong, S. C.; Li, T. S., Composite adaptive fuzzy output feedback control design for uncertain nonlinear strict-feedback systems with input saturation, IEEE Trans.Cybern., 45, 10, 2299-2308 (2015)
[32] Li, Y. M.; Tong, S. C., Prescribed performance adaptive fuzzy output-feedback dynamic surface control for nonlinear large-scale systems with time delays, Inf. Sci., 292, 125-142 (2015) · Zbl 1355.93100
[33] Li, Y. M.; Tong, S. C.; Li, T. S., Hybrid fuzzy adaptive output feedback control design for uncertain MIMO nonlinear systems with time-varying delays and input saturation, IEEE Trans. Fuzzy Syst. (2015)
[34] Li, Z. J.; Yang, C. G.; Su, C. Y.; Deng, S.; Sun, F. C.; Zhang, W. D., Decentralized fuzzy control of multiple cooperating robotic manipulators with impedance interaction, IEEE Trans. Fuzzy Syst., 23, 4, 1044-1056 (2015)
[35] Polycarpou, M. M., Stable adaptive neural control scheme for nonlinear systems, IEEE Trans. Autom. Control., 41, 3, 447-451 (1996) · Zbl 0846.93060
[36] Ren, B.; Ge, S. S.; Tee, K. P.; Lee, T. H., Adaptive neural control for output feedback nonlinear systems using a barrier lyapunov function, IEEE Trans. Neural Networks., 21, 8, 1339-1345 (2010)
[37] Smith, A.; Yang, C.; Ma, H.; Culverhouse, P.; Cangelosi, A.; Burdet, E., Novel hybrid adaptive controller for manipulation in complex pertubation environments, PLoS One., 10, 6, e0129281 (2015)
[38] Tong, S. C.; Zhang, L. L.; Li, Y. M., Observed-based adaptive fuzzy decentralized tracking control for switched uncertain nonlinear large-scale systems with dead zones, IEEE Trans. Syst. Man Cybern., 46, 1, 37-47 (2016)
[39] Tee, K. P.; Ge, S. S.; Tay, E. H., Barrier lyapunov functions for the control of output-constrained nonlinear systems, Automatica, 45, 4, 918-927 (2009) · Zbl 1162.93346
[40] Tee, K. P.; Ren, B.; Ge, S. S., Control of nonlinear systems with time-varying output constraints, Automatica., 47, 11, 2511-2516 (2011) · Zbl 1228.93069
[41] Tee, K. P.; Ge, S. S.; Tay, E. H., Adaptive control of electrostatic micro actuators with bidirectional drive, IEEE Trans. Control Syst. Technol., 17, 2, 340-352 (2009)
[42] Tong, S. C.; Sui, S.; Li, Y. M., Fuzzy adaptive output feedback control of MIMO nonlinear systems with partial tracking errors constrained, IEEE Trans. Fuzzy Syst., 23, 4, 729-742 (2015)
[43] Wang, L. X.; Mendel, J. M., Fuzzy basis functions, universal approximation, and orthogonal least-squares learning, IEEE Transactions on Neural Networks., 3, 5, 807-814 (1992)
[44] Wang, H.; Liu, X.; Liu, X.; Li, S., Robust adaptive fuzzy fault-tolerant control for a class of non-lower-triangular nonlinear systems with actuator failures, Inf. Sci., 336, 60-74 (2016) · Zbl 1394.93165
[45] Wu, J.; Chen, W.; Li, J., Fuzzy-approximation-based global adaptive control for uncertain strict-feedback systems with a priori known tracking accuracy, Fuzzy Sets Syst., 273, 8, 1-25 (2015) · Zbl 1373.93197
[46] Wu, J.; Li, J., Adaptive fuzzy control for perturbed strict-feedback nonlinear systems with predefined tracking accuracy, Nonlinear Dyn., 83, 3, 1185-1197 (2016) · Zbl 1351.93086
[47] Wu, J.; Chen, W. S.; Yang, F.; Li, J.; Zhu, Q., Global adaptive neural control for strict-feedback time-delay systems with predefined output accuracy, Inf. Sci., 301, 27-43 (2015) · Zbl 1360.93578
[48] Xia, Y. Q.; Yang, H. J.; Shi, P.; Fu, M. Y., Constrained infinite-horizon model predictive control for fuzzy discrete-time systems, IEEE Trans. Fuzzy Syst., 18, 2, 429-436 (2010)
[49] Yang, C.; Li, Z.; Cui, R.; Xu, B., Neural network-based motion control of an under-actuated wheeled inverted pendulum model, IEEE Trans. Neural Networks Learn.Syst., 25, 11, 2004-2016 (2014)
[50] Yang, C.; Wang, X.; Cheng, L.; Ma, H., Neural-learning based telerobot control with guaranteed performance, IEEE Trans. Cybern. (2016)
[51] Yang, C.; Jiang, Y.; Li, Z.; He, W.; Su, C.-Y., Neural control of bimanual robots with guaranteed global stability and motion precision, IEEE Trans. Ind. Inf.. (2016)
[52] Yang, C.; Wang, X.; Li, Z.; Li, Y.; Su, C.-Y., Teleoperation control based on combination of wave variable and neural networks, IEEE Trans. Syst. Man Cybern.. (2016)
[53] Zhang, T. P.; Wen, H.; Zhu, Q., Adaptive fuzzy control of nonlinear systems in pure feedback form based on input-to-state stability, IEEE Trans. Fuzzy Syst., 18, 1, 80-93 (2010)
[54] Zhou, B.; Li, Z. Y.; Lin, Z., Discrete-time \(L_∞\) and \(L_2\) norm vanishment and low gain feedback with their applications in constrained control, Automatica., 49, 1, 111-123 (2013) · Zbl 1258.93090
[55] Zhang, T. P.; Xia, X., Decentralized adaptive fuzzy output feedback control of stochastic nonlinear large-scale systems with dynamic uncertainties, Inf. Sci., 315, 17-38 (2015) · Zbl 1386.93036
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.