Adaptive fuzzy control for perturbed strict-feedback nonlinear systems with predefined tracking accuracy. (English) Zbl 1351.93086
Summary: In this paper, the tracking control problem for a class of nonlinear strict-feedback systems with disturbances is addressed. An adaptive fuzzy controller is developed by using the backstepping design technique based on a novel kind of nonnegative integral-type functions. In contrast to the existing results on the uncertain systems with additional disturbances, the features of the proposed control scheme are that it can guarantee the ultimate tracking error achieving an accuracy given a priori and the controller singularity problem is avoided completely. By introducing two novel \(n\)th-order continuously differentiable switching functions, the desired actual controller and the virtual control variables are obtained. The convergence of the tracking error is analyzed by using Barbalat’s lemma. It is shown that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. Finally, a simulation example is given to illustrate the effectiveness of the proposed control scheme.
MSC:
| 93C42 | Fuzzy control/observation systems |
| 92C10 | Biomechanics |
| 93C40 | Adaptive control/observation systems |
| 93B52 | Feedback control |
| 93C73 | Perturbations in control/observation systems |
Keywords:
uncertain strict-feedback systems; backstepping design technique; adaptive fuzzy control; Barbalat’s lemma; predefined tracking accuracyReferences:
| [1] | Ge, S.S., Li, G.Y., Lee, T.H.: Adaptive NN control for a class of strict-feedback discrete-time nonlinear systems. Automactica 39, 807-819 (2003) · Zbl 1023.93034 · doi:10.1016/S0005-1098(03)00032-3 |
| [2] | Zhang, T., Ge, S.S., Hang, C.C.: Stable adaptive control for a class of nonlinear systems using a modified Lyapunov function. IEEE Trans. Autom. Control 45(1), 129-132 (2000) · Zbl 0972.93061 · doi:10.1109/9.827369 |
| [3] | Zhang, T., Ge, S.S., Hang, C.C.: Adaptive neural network control for strict-feedback nonlinear systems using backstepping design. Automatica 36(12), 1835-1846 (2000) · Zbl 0976.93046 · doi:10.1016/S0005-1098(00)00116-3 |
| [4] | Wang, D., Huang, J.: Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form. IEEE Trans. Neural Netw. 16(1), 195-202 (2005) · doi:10.1109/TNN.2004.839354 |
| [5] | Li, T.S., Wang, D., Feng, G., Tong, S.C.: A DSC approach to robust adaptive NN tracking control for strict-feedback nonlinear systems. IEEE Trans. Syst. Man Cybern. Part B Cybern. 40(3), 915-927 (2010) · doi:10.1109/TSMCB.2009.2033563 |
| [6] | Xu, B., Shi, Z.K., Yang, C.G., Sun, F.C.: Composite neural dynamic surface control of a class of uncertain nonlinear systems in strict-feedback form. IEEE Trans. Cybern. 44(12), 2626-2634 (2014) · doi:10.1109/TCYB.2014.2311824 |
| [7] | Tong, S.C., Li, Y.M.: Observer-based fuzzy adaptive con- trol for strict-feedback nonlinear systems. Fuzzy Sets Syst. 160(12), 1749-1764 (2009) · Zbl 1175.93135 · doi:10.1016/j.fss.2008.09.004 |
| [8] | Wang, D., Huang, J.: Adaptive neural network control for a class of uncertain nonlinear systems in pure-feedback form. Automatica 38(8), 1365-1372 (2002) · Zbl 0998.93026 · doi:10.1016/S0005-1098(02)00034-1 |
| [9] | Ge, S.S., Yang, C.G., Lee, T.H.: Adaptive predictive control using neural network for a class of pure-feedback systems in discrete time. IEEE Trans. Neural Netw. 19(9), 1599-1614 (2008) · doi:10.1109/TNN.2008.2000446 |
| [10] | Zhang, T.P., Ge, S.S.: Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form. Automatica 44(7), 1895-1903 (2008) · Zbl 1149.93322 · doi:10.1016/j.automatica.2007.11.025 |
| [11] | 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) · doi:10.1109/TFUZZ.2009.2036906 |
| [12] | Yang, C.G., Ge, S.S., Cheng, X., Chai, T.Y., Lee, T.H.: Output feedback NN control for two classes of discrete-time systems with unknown control directions in a unified approach. IEEE Trans. Neural Netw. 19(11), 1873-1886 (2008) · doi:10.1109/TNN.2008.2003290 |
| [13] | Liu, Y.J., Tong, S., Wang, D., Li, T., Chen, C.: Adaptive neural output feedback controller design with reduced-order observer for a class of uncertain nonlinear SISO systems. IEEE Trans. Neural Netw. 22(8), 1328-1334 (2011) · doi:10.1109/TNN.2011.2159865 |
| [14] | Xu, B., Shi, Z.K., Yang, C.G.: Composite fuzzy control of a class of uncertain nonlinear systems with disturbance observer. Nonlinear dyn. 80(1—-2), 341-351 (2015). doi:10.1007/s11071-014-1872-5 · Zbl 1345.93109 · doi:10.1007/s11071-014-1872-5 |
| [15] | Liu, Y.J., Chen, C.L.P., Wen, G.X., Tong, S.C.: Adaptive neural output feedback tracking control for a class of uncertain discrete-time nonlinear systems. IEEE Trans. Neural Netw. 22(7), 1162-1167 (2011) · doi:10.1109/TNN.2011.2146788 |
| [16] | Liu, Y.J., Tong, S.C., Chen, C.L.P.: Adaptive fuzzy control via observer design for uncertain nonlinear systems with unmodeled dynamics. IEEE Trans. Fuzzy Syst. 21(2), 275-288 (2013) · doi:10.1109/TFUZZ.2012.2212200 |
| [17] | Chen, W., Jiao, L., Li, J., Li, R.: Adaptive NN backstepping output-feedback control for stochastic nonlinear strict-feedback systems with time-varying delays. IEEE Trans. Syst. Man Cybern. Part B Cybern. 40(3), 939-950 (2010) · doi:10.1109/TSMCB.2009.2033808 |
| [18] | Tong, S.C., Wang, T., Li, Y.M., Chen, B.: A combined backstepping and stochastic small-gain approach to robust adaptive fuzzy output feedback control. IEEE Trans. Fuzzy Syst. 21(2), 314-327 (2013) · doi:10.1109/TFUZZ.2012.2213260 |
| [19] | Wang, H., Chen, B., Lin, C.: Direct adaptive neural control for strict-feedback stochastic nonlinear systems. Nonlinear Dyn. 67(4), 2703-2718 (2012) · Zbl 1243.93108 · doi:10.1007/s11071-011-0182-4 |
| [20] | Chen, W., Li, J.: Decentralized output-feedback neural control for systems with unknown interconnections. IEEE Trans. Syst. Man Cybern. Part B Cybern. 38(1), 258-266 (2008) · doi:10.1109/TSMCB.2007.904544 |
| [21] | Tong, S.C., Liu, C.L., Li, Y.M.: Fuzzy-adaptive decentralized output-feedback control for large-scale nonlinear systems with dynamical uncertainties. IEEE Trans. Fuzzy Syst. 18(5), 845-861 (2010) · doi:10.1109/TFUZZ.2010.2050326 |
| [22] | Tong, S.C., Li, Y.M., Zhang, H.G.: Adaptive neural network decentralized backstepping output-feedback control for nonlinear large-scale systems with time delays. IEEE Trans. Neural Netw. 22(7), 1073-1086 (2011) · doi:10.1109/TNN.2011.2146274 |
| [23] | Chen, B., Liu, X.P.: Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by backstepping and application to chemical processes. IEEE Trans. Fuzzy Syst. 13(6), 832-847 (2005) · doi:10.1109/TFUZZ.2005.859322 |
| [24] | Chen, B., Liu, X.P., Tong, S.: Adaptive fuzzy output tracking control of MIMO nonlinear systems by backstepping approach. IEEE Trans. Fuzzy Syst. 15(2), 287-300 (2007) · doi:10.1109/TFUZZ.2006.880008 |
| [25] | Tong, S.C., Li, Y.M.: Adaptive fuzzy output feedback control of MIMO nonlinear systems with unknown dead-zone input. IEEE Trans. Fuzzy Syst. 21(1), 134-146 (2013) · doi:10.1109/TFUZZ.2012.2204065 |
| [26] | Chen, B., Liu, X., Liu, K., Lin, C.: Novel adaptiveneural control design for nonlinear MIMO time-delay systems. Automatica 45(6), 1554-1560 (2009) · Zbl 1166.93324 · doi:10.1016/j.automatica.2009.02.021 |
| [27] | Chen, M., Ge, S.S., How, B.: Robust adaptive neural network control for a class of uncertain MIMO nonlinear systems with input nonlinearities. IEEE Trans. Neural Netw. 21(5), 796-812 (2010) · doi:10.1109/TNN.2010.2042611 |
| [28] | 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 · doi:10.1016/j.automatica.2011.01.025 |
| [29] | Li, T.S., Tong, S.C., Feng, G.G.: A novel robust adaptive-fuzzy-tracking control for a class of nonlinearmulti-input/multi-output systems. IEEE Trans. Fuzzy Syst. 18(1), 150-160 (2010) · doi:10.1109/TFUZZ.2009.2038277 |
| [30] | Li, T.S., Wang, D., Chen, N.: Adaptive fuzzy control of uncertain MIMO non-linear systems in block-triangular forms. Nonlinear Dyn. 63(1-2), 105-123 (2011) · Zbl 1215.93077 · doi:10.1007/s11071-010-9789-0 |
| [31] | Ge, S.S., Hong, F., Lee, T.H.: Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients. IEEE Trans. Syst. Man Cybern. Part B Cybern. 34(1), 499-516 (2004) · doi:10.1109/TSMCB.2003.817055 |
| [32] | Wang, M., Chen, Bing, Shi, Peng: Adaptive neural control for a class of perturbed strict-feedback nonlinear time-delay systems. IEEE Trans. Syst. Man Cybern. Part B Cybern. 38(3), 721-730 (2008) · doi:10.1109/TSMCB.2008.918568 |
| [33] | Yoo, S.J., Park, J.B., Choi, Y.H.: Adaptive neural control for a class of strict-feedback nonlinear systems with state time delays. IEEE Trans. Neural Netw. 20(7), 1209-1215 (2009) · doi:10.1109/TNN.2009.2022159 |
| [34] | Li, T.S., Li, R.H., Li, J.F.: Decentralized adaptive neural control of nonlinear systems with unknown time delays. Nonlinear Dyn. 67(3), 2017-2026 (2012) · Zbl 1243.93010 · doi:10.1007/s11071-011-0126-z |
| [35] | Ho, D.W.C., Li, J., Niu, Y.: Adaptive neural control for a class of nonlinearly parametric time-delay systems. IEEE Trans. Neural Netw. 16(3), 625-635 (2005) · doi:10.1109/TNN.2005.844907 |
| [36] | Li, Y.M., Ren, C., Tong, S.: Adaptive fuzzy backstepping output feedback control of nonlinear uncertain time-delay systems based on high-gain filters. Nonlinear Dyn. 69(3), 781-792 (2012) · Zbl 1253.93073 · doi:10.1007/s11071-011-0304-z |
| [37] | Li, Y.M., Ren, C., Tong, S.: Adaptive fuzzy backstepping output feedback control for a class of MIMO time-delay nonlinear systems based on high-gain observer. Nonlinear Dyn. 67(2), 1175-1191 (2012) · Zbl 1243.93062 · doi:10.1007/s11071-011-0061-z |
| [38] | Huang, H., Feng, G., Cao, J.: Robust state estimation for uncertain neural networks with time-varying delay. IEEE Trans. Neural Netw. 19(8), 1329-1339 (2008) · doi:10.1109/TNN.2008.2000206 |
| [39] | Krstić, M., Deng, H.: Stabilization of Nonlinear Uncertain Systems. Springer, London (1998) · Zbl 0906.93001 |
| [40] | Wang, L.X., Mendel, J.M.: Fuzzy basis functions, universal approximation, and orthogonal least squares learning. IEEE Trans. Neural Netw. 3(5), 807-814 (1992) · doi:10.1109/72.159070 |
| [41] | Lewis, F.L., Yesildirek, A., Liu, K.: Multilayer neuralnet robot controller with guaranteed tracking performance. IEEE Trans. Neural Netw. 7(2), 388-399 (1996) · doi:10.1109/72.485674 |
| [42] | Niculescu, S.L.: Delay Effects on Stability: A Robust Control Approach. Springer, London (2001) · Zbl 0997.93001 |
| [43] | Yang, Y.S., Zhou, C.J.: Robust adaptive fuzzy control for a class of perturbed strict-feedback nonlinear systems via small-gain approach. Inf. Sci. 170(1-2), 211-234 (2005) · Zbl 1068.93037 · doi:10.1016/j.ins.2004.02.022 |
| [44] | Chen, W.S., 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 Netw. Learn. Syst. (2014). doi:10.1109/TNNLS.2014.2357451 |
| [45] | Wu, J., Chen, W.S., Li, J.: Fuzzy-approximation-based global adaptive control for uncertain strict-feedback systems with a priori known tracking accuracy. Fuzzy Sets Syst. 273, 1-25 (2015) · Zbl 1373.93197 · doi:10.1016/j.fss.2014.10.009 |
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.
