Single neural network approximation based adaptive control for a class of uncertain strict-feedback nonlinear systems. (English) Zbl 1268.92014
Summary: A new adaptive control design approach is presented for a class of uncertain strict-feedback nonlinear systems. In the controller design process, all unknown functions at intermediate steps are passed down, and only one neural network is used to approximate the lumped unknown function of the system at the last step. By this approach, the designed controller contains only one actual control law and one adaptive law, and can be given directly. Compared with existing methods, the structure of the designed controller is simpler and the computational burden is lighter. Stability analysis shows that all the closed-loop system signals are uniformly ultimately bounded, and the steady state tracking error can be made arbitrarily small by appropriately choosing control parameters. Simulation studies demonstrate the effectiveness and merits of the proposed approach.
MSC:
| 92B20 | Neural networks for/in biological studies, artificial life and related topics |
| 93C40 | Adaptive control/observation systems |
| 93B52 | Feedback control |
Keywords:
strict-feedback nonlinear systems; complexity growing problem; single neural network; adaptive controlReferences:
| [1] | Kanellakopoulos, I., Kokotovic, P.V., Morse, A.S.: Systematic design of adaptive controllers for feedback linearizable systems. IEEE Trans. Autom. Control 36(11), 1241-1253 (1991) · Zbl 0768.93044 · doi:10.1109/9.100933 |
| [2] | Krstic, M., Kanellakopoulos, I., Kokotovic, P.V.: Adaptive nonlinear control without overparametrization. Syst. Control Lett. 19(3), 177-185 (1992) · Zbl 0763.93043 · doi:10.1016/0167-6911(92)90111-5 |
| [3] | Seto, D., Annaswamy, A.M., Baillieul, J.: Adaptive control of nonlinear systems with a triangular structure. IEEE Trans. Autom. Control 39(7), 1411-1428 (1994) · Zbl 0806.93034 · doi:10.1109/9.299624 |
| [4] | Krstic, M., Kanellakopoulos, I., Kokotovic, P.V.: Nonlinear and Adaptive Control Design. Wiley, New York (1995) · Zbl 0763.93043 |
| [5] | Polycarpou, M.M.: Stable adaptive neural scheme for nonlinear systems. IEEE Trans. Autom. Control 41(3), 447-451 (1996) · Zbl 0846.93060 · doi:10.1109/9.486648 |
| [6] | Polycarpou, M.M., Mears, M.J.: Stable adaptive tracking of uncertainty systems using nonlinearly parameterized on-line approximators. Int. J. Control 70(3), 363-384 (1998) · Zbl 0945.93563 · doi:10.1080/002071798222280 |
| [7] | 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 |
| [8] | Kwan, C., Lewis, F.L.: Robust backstepping control of nonlinear systems using neural networks. IEEE Trans. Syst. Man Cybern., Part A, Syst. Hum. 30(6), 753-766 (2000) · doi:10.1109/3468.895898 |
| [9] | Ge, S.S., Wang, C.: Adaptive NN control of uncertain nonlinear pure-feedback systems. Automatica 38(4), 671-682 (2002) · Zbl 0998.93025 · doi:10.1016/S0005-1098(01)00254-0 |
| [10] | Ge, S.S., Wang, C.: Direct adaptive NN control of a class of nonlinear systems. IEEE Trans. Neural Netw. 13(1), 214-221 (2002) · doi:10.1109/72.977306 |
| [11] | 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 |
| [12] | Ge, S.S., Wang, C.: Adaptive neural control of uncertain MIMO nonlinear systems. IEEE Trans. Neural Netw. 15(3), 674-692 (2004) · doi:10.1109/TNN.2004.826130 |
| [13] | 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 |
| [14] | Wang, C., Hill, D.J., Ge, S.S., Chen, G.R.: An ISS-modular approach for adaptive neural control of pure-feedback systems. Automatica 42(5), 723-731 (2006) · Zbl 1137.93367 · doi:10.1016/j.automatica.2006.01.004 |
| [15] | Du, H., Shao, H., Yao, P.: Adaptive neural network control for a class of low-triangular-structured nonlinear systems. IEEE Trans. Neural Netw. 17(2), 509-514 (2006) · doi:10.1109/TNN.2005.863403 |
| [16] | 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 Netw. 21(8), 1339-1345 (2010) · doi:10.1109/TNN.2010.2047115 |
| [17] | Liu, Y.J., Tong, S.C., Li, Y.M.: Adaptive neural network tracking control for a class of nonlinear systems. Int. J. Syst. Sci. 40(2), 143-158 (2010) · Zbl 1292.93078 · doi:10.1080/00207720903042947 |
| [18] | Wen, G.X., Liu, Y.J., Tong, S.C., Li, X.L.: Adaptive neural output feedback control of nonlinear discrete-time systems. Nonlinear Dyn. 65(1), 65-75 (2011) · Zbl 1235.93110 · doi:10.1007/s11071-010-9874-4 |
| [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] | Swaroop, D.; Gerdes, J. C.; Yip, P. P.; Hedrick, J. K., Dynamic surface control of nonlinear systems, Albuquerque · Zbl 0981.83045 |
| [21] | Swaroop, D., Hedrick, J.K., Yip, P.P., Gerdes, J.C.: Dynamic surface control for a class of nonlinear systems. IEEE Trans. Autom. Control 45(10), 1893-1899 (2000) · Zbl 0991.93041 · doi:10.1109/TAC.2000.880994 |
| [22] | Yip, P.P., Hedrick, J.K.: Adaptive dynamic surface control: a simplified algorithm for adaptive backstepping control of nonlinear systems. Int. J. Control 71(5), 959-979 (1998) · Zbl 0969.93037 · doi:10.1080/002071798221650 |
| [23] | Wang, D., Huang, J.: Neural network based adaptive dynamic surface control for nonlinear systems in strict-feedback form. IEEE Trans. Neural Netw. 16(1), 195-202 (2005) · doi:10.1109/TNN.2004.839354 |
| [24] | 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. 19(10), 1712-1726 (2008) · doi:10.1109/TNN.2008.2001266 |
| [25] | 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 |
| [26] | Chen, W.S.: Adaptive backstepping dynamic surface control for systems with periodic disturbances using neural networks. IET Control Theory Appl. 3(10), 1383-1394 (2009) · doi:10.1049/iet-cta.2008.0322 |
| [27] | Chen, W.S., Jiao, L.C.: Adaptive tracking for periodically time-varying and nonlinearly parameterized systems using multilayer neural networks. IEEE Trans. Neural Netw. 21(2), 345-351 (2010) · doi:10.1109/TNN.2009.2038999 |
| [28] | Wang, M., Ge, S.S., Hong, K.S.: Approximation-based adaptive tracking control of pure-feedback nonlinear systems with multiple unknown time-varying delays. IEEE Trans. Neural Netw. 21(11), 1804-1816 (2010) · doi:10.1109/TNN.2010.2073719 |
| [29] | 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 |
| [30] | Wang, D.: Neural network-based adaptive dynamic surface control of uncertain nonlinear pure-feedback systems. Int. J. Robust Nonlinear Control 21(5), 527-541 (2011) · Zbl 1213.93105 · doi:10.1002/rnc.1608 |
| [31] | 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 |
| [32] | 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 |
| [33] | Kurdila, A.J., Narcowich, F.J., Ward, J.D.: Persistency of excitation in identification using radial basis function approximants. SIAM J. Control Optim. 33(2), 625-642 (1995) · Zbl 0831.93015 · doi:10.1137/S0363012992232555 |
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.
