Abstract
In this paper, the adaptive fixed-time control problem is investigated for a class of uncertain nonlinear systems with asymmetric time-varying full-state constraints. A nonlinear state-constrained function (NSCF) is constructed to prevent the asymmetric time-varying full-state constraints from being violated. Different from the conventional used full-state constraints method (such as the barrier Lyapunov function (BLF) approach), the asymmetric and symmetric full-state constraints problem can be solved without switching controller structure and no additional assumption about virtual control is required to be satisfied by the NSCF approach. To overcome the “explosion of complexity” problem of the traditional backstepping method, the fixed-time command filters (FTCFs) are used to propose the control strategy. Furthermore, error compensation mechanisms are designed to remove the filtering errors induced by utilizing the FTCFs. Under the backstepping control framework, an adaptive fixed-time control strategy is designed to ensure that all signals in the closed-loop system and tracking error are bounded within fixed-time, and all states are guaranteed to maintain in the predefined regions. Finally, a simulation example is given to illustrate the effectiveness of the proposed control scheme.
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References
Bi, W., Wang, T., Yu, X.: Fuzzy adaptive decentralized control for nonstrict-feedback large-scale switched fractional-order nonlinear systems. IEEE Trans. Cybern. 52(9), 8887–8896 (2022)
Deng, C., Yang, G.: Distributed adaptive fuzzy control for nonlinear multiagent systems under directed graphs. IEEE Trans. Fuzzy Syst. 26(3), 1356–1366 (2017)
Fuentes-Aguilar, R.Q., Chairez, I.: Adaptive tracking control of state constraint systems based on differential neural networks: A barrier lyapunov function approach. IEEE Trans. Neural Netw. Learn. Syst. 31(12), 5390–5401 (2020)
Gao, M., Ding, L., Jin, X.: Elm-based adaptive faster fixed-time control of robotic manipulator systems. IEEE Trans. Neural Netw. Learn. Syst. (2021). https://doi.org/10.1109/TNNLS.2021.3116958
Huo, X., Karimi, H.R., Zhao, X., Wang, B., Zong, G.: Adaptive-critic design for decentralized event-triggered control of constrained nonlinear interconnected systems within an identifier-critic framework. IEEE Trans. Cybern. (2021). https://doi.org/10.1109/TCYB.2020.3037321
Jiang, B., Hu, Q., Friswell, M.I.: Fixed-time attitude control for rigid spacecraft with actuator saturation and faults. IEEE Trans. Control Syst. Technol. 24(5), 1892–1898 (2016)
Jin, X., Lü, S., Yu, J.: Adaptive NN-based consensus for a class of nonlinear multiagent systems with actuator faults and faulty networks. IEEE Trans. Neural Netw. Learn. Syst. (2021). https://doi.org/10.1109/TNNLS.2021.3053112
Kang, S., Liu, P.X., Wang, H.: Command filter-based adaptive fuzzy decentralized control for large-scale nonlinear systems. Nonlinear Dyn. 105(4), 3239–3253 (2021)
Kong, L., Yu, X., Zhang, S.: Neuro-learning-based adaptive control for state-constrained strict-feedback systems with unknown control direction. ISA Trans. 112, 12–22 (2021)
Li, H., Zhang, Z., Yan, H., Xie, X.: Adaptive event-triggered fuzzy control for uncertain active suspension systems. IEEE Trans. Cybern. 49(12), 4388–4397 (2018)
Li, X., Yan, J., Yang, G.: Adaptive fault estimation for T-S fuzzy interconnected systems based on persistent excitation condition via reference signals. IEEE Trans. Cybern. 49(8), 2822–2834 (2018)
Liang, Y., Li, Y., Che, W., Hou, Z.: Adaptive fuzzy asymptotic tracking for nonlinear systems with nonstrict-feedback structure. IEEE Trans. Cybern. 51(2), 853–861 (2021)
Lin, G., Li, H., Ahn, C.K., Yao, D.: Event-based finite-time neural control for human-in-the-loop UAV attitude systems. IEEE Trans. Neural Netw. Learn. Syst. (2022). https://doi.org/10.1109/TNNLS.2022.3166531
Liu, G., Liang, H., Pan, Y., Ahn, C.K.: Antagonistic interaction-based bipartite consensus control for heterogeneous networked systems. IEEE Trans. Syst. Man Cybern.: Syst. (2022). https://doi.org/10.1109/TSMC.2022.3167120
Liu, H., Li, X., Deng, C., Ahn, C.K.: Fault estimation and control for unknown discrete-time systems based on data-driven parameterization approach. IEEE Trans. Cybern. (2021). https://doi.org/10.1109/TCYB.2021.3107425
Liu, L., Chen, A., Liu, Y.: Adaptive fuzzy output-feedback control for switched uncertain nonlinear systems with full-state constraints. IEEE Trans. Cybern. (2021). https://doi.org/10.1109/TCYB.2021.3050510
Liu, L., Liu, Y., Li, D., Tong, S., Wang, Z.: Barrier Lyapunov function-based adaptive fuzzy FTC for switched systems and its applications to resistance-inductance-capacitance circuit system. IEEE Trans. Cybern. 50(8), 3491–3502 (2019)
Ma, Y., Che, W., Deng, C., Wu, Z.: Distributed model-free adaptive control for learning nonlinear MASs under DoS attacks. IEEE Trans. Neural Netw. Learn. Syst. (2021). https://doi.org/10.1109/TNNLS.2021.3104978
Qian, C., Lin, W.: A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE Trans. Autom. Control 46(7), 1061–1079 (2001)
Qin, H., Yang, H., Sun, Y., Zhang, Y.: Adaptive interval type-2 fuzzy fixed-time control for underwater walking robot with error constraints and actuator faults using prescribed performance terminal sliding-mode surfaces. Int. J. Fuzzy Syst. 23(4), 1137–1149 (2021)
Ren, P., Wang, F., Zhu, R.: Adaptive fixed-time fuzzy control of uncertain nonlinear quantized systems. Int. J. Fuzzy Syst. 23(3), 794–803 (2021)
Shi, X., Cheng, Y., Yin, C., Huang, X., Zhong, S.: Design of adaptive backstepping dynamic surface control method with RBF neural network for uncertain nonlinear system. Neurocomputing 330, 490–503 (2019)
Shi, X., Zhou, Z., Zhou, D., Li, R., Chen, X.: Observer-based event-triggered fixed-time control for nonlinear system with full-state constraints and input saturation. Int. J. Control 95(2), 432–446 (2022)
Shotorbani, A.M., Mohammadi-Ivatloo, B., Wang, L., Marzband, M., Sabahi, M.: Application of finite-time control Lyapunov function in low-power PMSG wind energy conversion systems for sensorless MPPT. Int. J. Electr. Power Energy Syst. 106, 169–182 (2019)
Sui, S., Tong, S.: Finite-time fuzzy adaptive ppc for nonstrict-feedback nonlinear mimo systems. IEEE Trans. Cybern. 53, 732–742 (2022). https://doi.org/10.1109/TCYB.2022.3163739
Sui, S., Tong, S.: Finite-time fuzzy adaptive PPC for nonstrict-feedback nonlinear MIMO systems. IEEE Trans. Cybern. (2022). https://doi.org/10.1109/TCYB.2022.3163739
Wang, L., Liu, P.X., Wang, H.: Fast finite-time control for nonaffine stochastic nonlinear systems against multiple actuator constraints via output feedback. IEEE Trans. Cybern. (2022). https://doi.org/10.1109/TCYB.2022.3177587
Wang, N., Gao, Y., Yang, C., Zhang, X.: Reinforcement learning-based finite-time tracking control of an unknown unmanned surface vehicle with input constraints. Neurocomputing 484, 26–37 (2022)
Wang, Y., Xu, N., Liu, Y., Zhao, X.: Adaptive fault-tolerant control for switched nonlinear systems based on command filter technique. Appl. Math. Comput. 392, 125725 (2021)
Wang, Z., Chen, Z., Zhang, Y., Yu, X., Wang, X., Liang, B.: Adaptive finite-time control for bilateral teleoperation systems with jittering time delays. Int. J. Robust Nonlinear Control 29(4), 1007–1030 (2019)
Wei, Y., Karimi, H.R.: Dynamic sliding mode control for nonlinear parameter-varying systems. Int. J. Robust Nonlinear Control 31(17), 8408–8419 (2021)
Wu, Y., Wang, Z.: Fuzzy adaptive practical fixed-time consensus for second-order nonlinear multiagent systems under actuator faults. IEEE Trans. Cybern. 51(3), 1150–1162 (2020)
Xi, C., Dong, J.: Adaptive reliable guaranteed performance control of uncertain nonlinear systems by using exponent-dependent barrier Lyapunov function. Int. J. Robust Nonlinear Control 29(4), 1051–1062 (2019)
Xia, J., Lian, Y., Su, S., Shen, H., Chen, G.: Observer-based event-triggered adaptive fuzzy control for unmeasured stochastic nonlinear systems with unknown control directions. IEEE Trans. Cybern. 52(10), 10655–10666 (2022)
Xie, X., Lu, J., Yue, D., Ding, D.: Enhanced fuzzy fault estimation of discrete-time nonlinear systems via a new real-time gain-scheduling mechanism. IEEE Trans. Cybern. (2021). https://doi.org/10.1109/TCYB.2021.3107040
Xie, X., Wei, C., Gu, Z., Shi, K.: Relaxed resilient fuzzy stabilization of discrete-time Takagi-Sugeno systems via a higher order time-variant balanced matrix method. IEEE Trans. Fuzzy Syst. (2022). https://doi.org/10.1109/TFUZZ.2022.3145809
Yang, H., Ye, D.: Adaptive fuzzy nonsingular fixed-time control for nonstrict-feedback constrained nonlinear multiagent systems With input saturation. IEEE Trans. Fuzzy Syst. 29(10), 3142–3153 (2020)
Yao, D., Li, H., Lu, R., Shi, Y.: Event-triggered guaranteed cost leader-following consensus control of second-order nonlinear multiagent systems. IEEE Trans. Syst. Man Cybern.: Syst. 52(4), 2615–2624 (2021)
Yao, D., Li, H., Shi, Y.: Adaptive event-triggered sliding mode control for consensus tracking of nonlinear multi-agent systems with unknown perturbations. IEEE Trans. Cybern. (2022). https://doi.org/10.1109/TCYB.2022.3172127
Ye, D., Zou, A., Sun, Z.: Predefined-time predefined-bounded attitude tracking control for rigid spacecraft. IEEE Trans. Aerosp. Electron. Syst. 58(1), 464–472 (2021)
Yu, J., Chen, B., Yu, H., Lin, C., Zhao, L.: Neural networks-based command filtering control of nonlinear systems with uncertain disturbance. Inf. Sci. 426, 50–60 (2018)
Zhang, L., Ding, H., Shi, J., Huang, Y., Chen, H., Guo, K., Li, Q.: An adaptive backstepping sliding mode controller to improve vehicle maneuverability and stability via torque vectoring control. IEEE Trans. Veh. Technol. 69(3), 2598–2612 (2020)
Zhao, J., Tong, S., Li, Y.: Observer-based fuzzy adaptive control for mimo nonlinear systems with non-constant control gain and input delay. IET Control Theory Appl. 15(11), 1488–1505 (2021)
Zhao, L., Yu, J., Lin, C., Yu, H.: Distributed adaptive fixed-time consensus tracking for second-order multi-agent systems using modified terminal sliding mode. Appl. Math. Comput. 312, 23–35 (2017)
Zhu, Z., Liang, H., Liu, Y., Xue, H.: Command filtered event-triggered adaptive control for MIMO stochastic multiple time-delay systems. Int. J. Robust Nonlinear Control 32(2), 715–736 (2022)
Zhuang, H., Sun, Q., Chen, Z., Zeng, X.: Robust adaptive sliding mode attitude control for aircraft systems based on back-stepping method. Aerosp. Sci. Technol. 118, 107069 (2021)
Acknowledgements
This work was supported by the Natural Science Foundation of China (61833009, 61690212), Natural Science Foundation of Shaanxi Province of China (2022JQ-636), and Special Scientific Research Plan Project of Shaanxi Province Education Department (21JK0905).
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Liu, R., Liu, M., Shi, Y. et al. Adaptive Fixed-Time Fuzzy Control for Uncertain Nonlinear Systems with Asymmetric Time-Varying Full-State Constraints. Int. J. Fuzzy Syst. 25, 1597–1611 (2023). https://doi.org/10.1007/s40815-023-01461-w
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DOI: https://doi.org/10.1007/s40815-023-01461-w