Abstract
This paper studies the adaptive tracking control problem for a class of nonstrict feedback nonlinear systems with quantized inputs and actuator faults. Compared with existing works on quantized control problem, the asymmetric hysteresis quantizer is considered in the actuator failure problem in this paper. To resolve the control challenge caused by the quantization effect, a nonlinear decomposition of the quantizer is proposed and applied to the controller design in the last step of the backstepping-based control approach. Combining with fuzzy logic systems, the unknown nonlinear functions contained in the researched nonlinear system is disposed without knowing some restrictive conditions of uncertainties. The developed controller guarantees that the system output converges to a small neighborhood of the desired reference signal and all the signals of the closed-loop system are bounded. Finally, simulation results are depicted to illustrate the efficiency of the proposed control algorithm.
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Wu, Z.G., Shi, P., Su, H.Y.: Reliable \(H_\infty\) control for discrete-time fuzzy systems with infinite-distributed delay. IEEE Trans. Fuzzy Syst. 20(1), 22–31 (2012)
Zhang, Y.M., Jiang, J.: Bibliographical review on reconfigurable fault-tolerant control systems. Annu. Rev. Control 32(2), 229–252 (2008)
Zhao, Q., Jiang, J.: Reliable state feedback control system design against actuator failures. Automatica 34(10), 1267–1272 (1998)
Tao, G., Joshi, S.M., Ma, X.L.: Adaptive state feedback and tracking control of systems with actuator failures. IEEE Trans. Autom. Control 46(1), 78–95 (2001)
Li, B.Y., Du, H.P., Li, W.H.: Fault-tolerant control of electric vehicles with in-wheel motors using actuator-grouping sliding mode controllers. Mech. Syst. Signal Process. 72–73, 462–485 (2016)
Boskovic, J.D., Mehra, R.K.: Multiple-model adaptive flight control scheme for accommodation of actuator failures. J. Guid. Control Dyn. 25(4), 712–724 (2002)
Xing, L.T., Wen, C.Y., Liu, Z.T., Su, H.Y., Cai, J.P.: Adaptive compensation for actuator failures with event-triggered input. Automatica 85, 129–136 (2017)
Zhang, J.X., Yang, G.H.: Prescribed performance fault-tolerant control of uncertain nonlinear systems with unknown control directions. IEEE Trans. Autom. Control 62(12), 6529–6535 (2017)
Li, Y.X., Yang, G.H.: Robust fuzzy adaptive fault-tolerant control for a class of nonlinear systems with mismatched uncertainties and actuator faults. Nonlinear Dyn. 81(1–2), 395–409 (2015)
Wang, J.H., Liu, Z., Chen, C.L.P., Zhang, Y.: Fuzzy adaptive compensation control of uncertain stochastic nonlinear systems with actuator failures and input hysteresis. IEEE Trans. Cybern. 49(1), 2–13 (2019)
Wang, L.J., Basin, M.V., Li, H.Y., Lu, R.Q.: Observer-based composite adaptive fuzzy control for nonstrict-feedback systems with actuator failures. IEEE Trans. Fuzzy Syst. 26(4), 2336–2347 (2018)
Li, Y.M., Sun, K.K., Tong, S.C.: Adaptive fuzzy robust fault-tolerant optimal control for nonlinear large-scale systems. IEEE Trans. Fuzzy Syst. 26(5), 2899–2914 (2018)
Li, Y.M., Ma, Z.Y., Tong, S.C.: Adaptive fuzzy output-constrained fault-tolerant control of nonlinear stochastic large-scale systems with actuator faults. IEEE Trans. Cybern. 47(9), 2362–2376 (2017)
Zhang, C.H., Hong, G.Y.: Event-triggered adaptive output feedback control for a class of uncertain nonlinear systems with actuator failures. IEEE Trans. Cybern. 50(1), 201–210 (2020)
Wang, F., Liu, Z., Zhang, Y., Chen, C.L.P.: Adaptive finite-time control of stochastic nonlinear systems with actuator failures. Fuzzy Sets Syst. 374(1), 170–183 (2019)
Niu, J., Chen, F.Y., Tao, G.: Nonlinear fuzzy fault-tolerant control of hypersonic flight vehicle with parameteric uncertainty and actuator fault. Nonlinear Dyn. 92(3), 1299–1315 (2018)
Mushage, B.O., Chedjou, J.C., Kyamakya, K.: Fuzzy neural network and observer-based fault tolerant adaptive nonlinear control of uncertain 5-DOF upper-limb exoskeleton robot for passive rehabilitation. Nonlinear Dyn. 87(3), 2021–2037 (2017)
Cai, M.J., Xiang, Z.G., Guo, J.: Adaptive finite-time fault-tolerant consensus protocols for multiple mechanical systems. J. Franklin Inst. 353(6), 1386–1408 (2016)
Ishii, H., Francis, B.: Limited Data Rate in Control Systems With Network. Springer, Berlin, Germany (2002)
Miller, R.K., Michell, A.N., Farrel, J.A.: Quantizer effects on steady state error specifications of digital feedback control systems. IEEE Trans. Autom. Control 34(6), 651–654 (1989)
Lunze, J., Nixdorf, B., Schröder, J.: Deterministic discrete-event representations of linear continuous variable systems. Automatica 35(3), 395–406 (1999)
Gao, H.J., Chen, T.W.: A new approach to quantized feedback control systems. Automatica 44(2), 534–542 (2008)
Persis, C.D.: Robust stabilization of nonlinear systems by quantized and ternary control. Syst. Control Lett. 58(8), 602–609 (2009)
Liu, T.F., Jiang, Z.P., Hill, D.J.: A sector bound approach to feedback control of nonlinear systems with state quantization. Automatica 48(1), 145–152 (2012)
Hayakawa, T., Ishii, H., Tsumura, K.: Adaptive quantized control for linear uncertain discrete-time systems. Automatica 45, 692–700 (2009)
Hayakawa, T., Ishii, H., Tsumura, K.: Adaptive quantized control for nonlinear uncertain systems. Syst. Control Lett. 58(9), 625–632 (2006)
Zhou, J., Wen, C.Y., Yang, G.H.: Adaptive backstepping stabilization of nonlinear uncertain systems with quantized input signal. IEEE Trans. Autom. Control 59(2), 460–464 (2014)
Yu, X.W., Lin, Y.: Adaptive backstepping quantized control for a class of nonlinear systems. IEEE Trans. Autom. Control 62(2), 981–985 (2017)
Xing, L.T., Wen, C.Y., Su, H.Y., Cai, J.P., Wang, L.: A new adaptive control scheme for uncertain nonlinear systems with quantized input signal. J. Franklin Inst. 352(12), 5599–5610 (2015)
Xing, L.T., Wen, C.Y., Su, H.Y., Liu, Z.T., Cai, J.P.: Robust control for a class of uncertain nonlinear systems with input quantization. Int. J. Robust Nonlinear Control 26(8), 1585–1596 (2016)
Liu, Z., Wang, F., Zhang, Y., Chen, C.L.P.: Fuzzy adaptive quantized control for a class of stochastic nonlinear uncertain systems. IEEE Trans. Cybern. 46(2), 524–534 (2016)
Wang, F., Liu, Z., Zhang, Y., Chen, C.L.P.: Adaptive quantized controller design via backstepping and stochastic small-gain approach. IEEE Trans. Fuzzy Syst. 24(2), 330–343 (2016)
Jin, X.: Adaptive fault tolerant control for a class of input and state constrained MIMO nonlinear systems. Int. J. Robust Nonlinear Control 26(2), 286–302 (2016)
Su, H., Zhang, W.H.: Adaptive fuzzy FTC design of nonlinear stochastic systems with actuator faults and unmodeled dynamics. Int. J. Adapt. Control Signal Process. 32(7), 1081–1101 (2018)
Lai, G.Y., Liu, Z., Zhang, Y., Chen, C.L.P., Xie, S.L.: Asymmetric actuator backlash compensation in quantized adaptive control of uncertain networked nonlinear systems. IEEE Trans. Neural Netw. Learn. Syst. 28(2), 294–307 (2017)
Polycarpou, M.M.: Stable adaptive neural control scheme for nonlinear systems. IEEE Trans. Autom. Control 41(3), 447–451 (1996)
Chen, B., Liu, X.P., Liu, K.F., Lin, C.: Direct adaptive fuzzy control of nonlinear strict-feedback systems. Automatica 45(6), 1530–1535 (2009)
Wang, L.X.: Stable adaptive fuzzy control of nonlinear systems. IEEE Trans. Fuzzy Syst. 1(2), 146–155 (1993)
Tong, S.C., Li, Y.M., Sui, S.: Adaptive fuzzy tracking control design for SISO uncertain non-strict feedback nonlinear systems. IEEE Trans. Fuzzy Syst. 24(6), 1441–1454 (2016)
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Nos. 61973198, 61633014, 61703248), the Research Fund for the Taishan Scholar Project of Shandong Province of China, and SDUST Research Fund (No. 2015TDJH105).
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Su, H., Zhang, W. Fuzzy Quantized Control of Nonstrict Feedback Nonlinear Systems with Actuator Faults. Int. J. Fuzzy Syst. 22, 1922–1936 (2020). https://doi.org/10.1007/s40815-020-00891-0
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DOI: https://doi.org/10.1007/s40815-020-00891-0