Adaptive neural network tracking design for a class of uncertain nonlinear discrete-time systems with dead-zone. (English) Zbl 1336.93096
Summary: In this paper, the stability and control issues of a class of uncertain nonlinear discrete-time systems in the strict feedback form are investigated. The dead-zone input in the systems, whose property is non-symmetric and discretized, is investigated. The unknown functions in the systems are approximated by using the Radial Basis Function Neural Networks (RBFNNs). Backstepping design procedure is employed in the controller and the adaptation laws design. Lyapunov analysis method is utilized to prove the stability of the closed-loop system. A simulation example is given to illustrate the effectiveness of the proposed approach.
MSC:
| 93C42 | Fuzzy control/observation systems |
| 93C40 | Adaptive control/observation systems |
| 92B20 | Neural networks for/in biological studies, artificial life and related topics |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 93C10 | Nonlinear systems in control theory |
| 93C55 | Discrete-time control/observation systems |
Keywords:
adaptive control; RBF neural network; non-symmetric dead-zone; backstepping design; uncertain nonlinear systemsReferences:
| [1] | Zhang H G, Wang Y, Liu D. Delay-dependent guaranteed cost for uncertain stochastic fuzzy systems with multiple time delays. IEEE Trans Syst Man Cybern Part B: Cybern, 2008, 38: 126-140 · doi:10.1109/TSMCB.2007.910532 |
| [2] | Xu X H, Zhang J Y, Zhang W H. Mean square exponential stability of stochastic neural network with reaction-diffusion terms and delays. Appl Math Lett, 2011, 24: 5-11 · Zbl 1213.93200 · doi:10.1016/j.aml.2010.07.002 |
| [3] | Wang Z S, Zhang H G, Li P. An LMI approach to stability analysis of reaction-diffusion Cohen-Grossberg neural networks concerning with Dirichlet boundary conditions and distributed delays. IEEE Trans Syst Man Cybern Part B: Cybern, 2010, 40: 1596-1606 · doi:10.1109/TSMCB.2010.2043095 |
| [4] | Dong J X, Yang G H. H infinity controller synthesis via switched PDC scheme for discrete-time T-S fuzzy systems. IEEE Trans Fuzzy Syst, 2009, 17: 544-555 · doi:10.1109/TFUZZ.2008.924328 |
| [5] | Zhang H G, Quan Y B. Modeling, identification, and control of a class of nonlinear systems. IEEE Trans Fuzzy Syst, 2001, 9: 349-354 · doi:10.1109/91.919256 |
| [6] | Tong S C, Li C Y, Li Y M. Fuzzy adaptive observer backstepping control for MIMO nonlinear systems. Fuzzy Sets Syst, 2009, 160: 2755-2775 · Zbl 1176.93049 · doi:10.1016/j.fss.2008.09.004 |
| [7] | Tong S C, He X L, Zhang H G. A combined backstepping and small-gain approach to robust adaptive fuzzy output feedback control. IEEE Trans Fuzzy Syst, 2009, 17: 1059-1069 · doi:10.1109/TFUZZ.2009.2021648 |
| [8] | Chen W S, Li J M. Decentralized output-feedback neural control for systems with unknown interconnections. IEEE Trans Syst Man Cybern Part B: Cybern, 2008, 38: 258-266 · doi:10.1109/TSMCB.2007.904544 |
| [9] | Chen W S, Jiao L C, Li J, et al. Adaptive NN backstepping output-feedback control for stochastic nonlinear strictfeedback systems with time-varying delays. IEEE Trans Syst Man Cybern Part B: Cybern, 2010, 40: 939-950 · doi:10.1109/TSMCB.2009.2033808 |
| [10] | Chen M, Ge S S, Ren B B. robust adaptive neural network control for a class of uncertain MIMO nonlinear systems with input nonlinearities. IEEE Trans Neur Netw, 2010, 21: 796-812 · doi:10.1109/TNN.2010.2042611 |
| [11] | Yoo S J, Park J B. Neural-network-based decentralized adaptive control for a class of large-scale nonlinear systems with unknown time-varying delays. IEEE Trans Syst Man Cybern Part B: Cybern, 2009, 39: 1316-1323 |
| [12] | Li Z J, Cao X Q, Ding N. Adaptive fuzzy control for synchronization of nonlinear teleoperators with stochastic timevarying communication delays. IEEE Trans Fuzzy Syst, 2011, 19: 745-757 · doi:10.1109/TFUZZ.2011.2143417 |
| [13] | Chen M, Ge S S, Ren B B. Robust attitude control of helicopters with actuator dynamics using neural networks. IET Contr Theory Appl, 2010, 4: 2837-2854 · doi:10.1049/iet-cta.2009.0478 |
| [14] | Chen M, Jiang B, Zou J, et al. Robust adaptive tracking control of the underwater robot with input nonlinearity using neural networks. Int J Comput Intell Syst, 2010, 3: 646-655 · doi:10.1080/18756891.2010.9727730 |
| [15] | Tong S C, Li Y M. Robust adaptive fuzzy backstepping output feedback tracking control for nonlinear system with dynamic uncertainties. Sci China Inf Sci, 2010, 53: 307-324 · Zbl 1497.93134 · doi:10.1007/s11432-010-0031-y |
| [16] | Li T S, Wang D, Feng G. A DSC approach to robust adaptive NN tracking control for strict-feedback nonlinear systems. IEEE Trans Syst Man Cybern Part B: Cybern, 2010, 40: 915-927 · doi:10.1109/TSMCB.2009.2033563 |
| [17] | Tong S C, Ren C E, Li Y M. Adaptive fuzzy decentralized control for nonlinear large-scale systems based on high-gain observer. Sci China Inf Sci, 2012, 55: 228-242 · doi:10.1007/s11432-011-4404-7 |
| [18] | Li H X, Tong S C. A hybrid adaptive fuzzy control for a class of nonlinear MIMO systems. IEEE Trans Fuzzy Syst, 2003 11: 24-34 · doi:10.1109/TFUZZ.2002.806314 |
| [19] | Wang M, Zhang S Y, Chen B, et al. Direct adaptive neural control for stabilization of nonlinear time-delay systems. Sci China Inf Sci, 2010, 53: 800-812 · Zbl 1497.93123 · doi:10.1007/s11432-010-0075-z |
| [20] | Li Z J, Adaptive neural-fuzzy control of uncertain constrained multiple coordinated nonholonomic mobile manipulators. Eng Appl Artif Intell, 2008, 21: 985-1000 · doi:10.1016/j.engappai.2007.08.007 |
| [21] | Li Z J, Xu C Q. Adaptive fuzzy logic control of dynamic balance and motion for wheeled inverted pendulums. Fuzzy Sets Syst, 2009, 160: 1787-1803 · Zbl 1175.93129 · doi:10.1016/j.fss.2008.09.013 |
| [22] | Yoo S J, Park J B, Choi Y H. Adaptive output feedback control of flexible-joint robots using neural networks: dynamic surface design approach. IEEE Trans Neural Netw, 2008, 19: 1712-1726 · doi:10.1109/TNN.2008.2001266 |
| [23] | Ge S S, Li G Y, Lee T H. Adaptive NN control for a class of strict-feedback discrete-time nonlinear systems. Automatica, 2003, 39: 807-819 · Zbl 1023.93034 · doi:10.1016/S0005-1098(03)00032-3 |
| [24] | Jagannathan S, Lewis F L. Discrete-time neural net controller for a class of nonlinear dynamical systems. IEEE Trans Autom Control, 1996, 41: 1693-1699 · Zbl 0872.93046 · doi:10.1109/9.544013 |
| [25] | Ge S S, Li G Y, Zhang J, et al. Direct adaptive control for a class of MIMO nonlinear systems using neural networks. IEEE Trans Autom Control, 2004, 49: 2001-2006 · Zbl 1365.93262 · doi:10.1109/TAC.2004.837561 |
| [26] | Ge S S, Zhang J, Lee T H. State feedback neural network control of a class of discrete MIMO nonlinear systems with disturbances. IEEE Trans Syst Man Cybern Part B: Cybern, 2004, 34: 1630-1645 · doi:10.1109/TSMCB.2004.826827 |
| [27] | Li H X, Deng H. An approximate internal model based neural control for unknown nonlinear discrete processes. IEEE Trans Neural Netw, 2006, 17: 659-670 · doi:10.1109/TNN.2006.873277 |
| [28] | Yang C G, Ge S S, Xiang C, et al. Output feedback NN control for two classes of discrete-time systems with unknown control directions in a unified approach. IEEE Trans Neural Netw, 2008, 19: 1873-1886 · doi:10.1109/TNN.2008.2003290 |
| [29] | Zhou J, Shen X Z. Robust adaptive control of nonlinear uncertain plants with unknown dead-zone. IEE Proc Control Theory Appl, 2007, 1: 25-32 · doi:10.1049/iet-cta:20050240 |
| [30] | Yoo S J, Park J B, Choi Y H. Decentralized adaptive stabilization of interconnected nonlinear systems with unknown non-symmetric dead-zone inputs. Automatica, 2009, 45: 436-443 · Zbl 1158.93399 · doi:10.1016/j.automatica.2008.07.019 |
| [31] | Wang X S, Su C Y, Hong H. Robust adaptive control of a class of linear systems with unknown dead-zone. Automatica, 2004, 40: 407-413 · Zbl 1036.93036 · doi:10.1016/j.automatica.2003.10.021 |
| [32] | Zhou J, Wen C, Zhang Y. Adaptive output control of nonlinear systems with uncertain dead zone nonlinearity. IEEE Trans Autom Control, 2006, 51: 504-511 · Zbl 1366.93306 · doi:10.1109/TAC.2005.864200 |
| [33] | Ibrir S, Xie W F, Su C Y. Adaptive tracking of nonlinear systems with non-symmetric dead-zone input. Automatica, 2007, 43: 522-530 · Zbl 1137.93350 · doi:10.1016/j.automatica.2006.09.022 |
| [34] | Lewis F L, Tim W K, Wang L Z, et al. Dead-zone compensation in motion control systems using adaptive fuzzy logic control. IEEE Trans Control Syst Technol, 1999, 7: 731-741 · doi:10.1109/87.799674 |
| [35] | Selmic R R, Lewis F L. Dead-zone compensation in motion control systems using neural networks. IEEE Trans Autom Control, 2000, 45: 602-613 · Zbl 0989.93068 · doi:10.1109/9.847098 |
| [36] | Tong S C, Li Y M. Adaptive fuzzy output feedback tracking backstepping control of strict-feedback nonlinear systems with unknown dead zones. IEEE Trans Fuzzy Syst, 2012, 20: 168-180 · doi:10.1109/TFUZZ.2011.2171189 |
| [37] | Chen M, Ge S S, Ren B B. Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints. Automatica, 2011, 47: 452-465 · Zbl 1219.93053 · doi:10.1016/j.automatica.2011.01.025 |
| [38] | Chen, M.; Ge, S. S.; How, B. V.; etal., Robust adaptive position mooring control for marine vessels (2012) |
| [39] | Tao G, Kokotovic P V. Discrete-time adaptive control of plants with unknown output dead-zones. Automatica, 1995, 31: 287-291 · Zbl 0821.93046 · doi:10.1016/0005-1098(94)00087-Y |
| [40] | Campos J, Lewis F L. Dead-zone compensation in discrete-time using adaptive fuzzy logic. IEEE Trans Fuzzy Syst, 1999, 7: 697-707 · doi:10.1109/91.811238 |
| [41] | Zhang, X.; Zhang, H. G.; Liu, D. R.; etal., Neural-network-based reinforcement learning controller for nonlinear systems with non-symmetric dead-zone inputs, 124-129 (2009) · doi:10.1109/ADPRL.2009.4927535 |
| [42] | Deolia, V. K.; Purwar, S.; Sharma, T. N., Backstepping control of discrete-time nonlinear system under unknown dead-zone constraint, 344-349 (2011) |
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.
