Prescribed-time stabilisation design for a class of nonlinear systems with state constraints

References

• Arcak, M., Seron, M., Braslavsky, J., & Kokotovic, P. (2000). Robustification of backstepping against input unmodeled dynamics. IEEE Transactions on Automatic Control, 45(7), 1358–1363. https://doi.org/10.1109/9.867048
   Web of Science ®Google Scholar
• Bemporad, A. (1998). Reference governor for constrained nonlinear systems. IEEE Transactions on Automatic Control, 43(3), 415–419. https://doi.org/10.1109/9.661611
   Web of Science ®Google Scholar
• Bhat, S. P., & Bernstein, D. S. (2000). Finite-time stability of continuous autonomous systems. SIAM Journal on Control and Optimization, 38(3), 751–766. https://doi.org/10.1137/S0363012997321358
   Web of Science ®Google Scholar
• Cai, M., & Xiang, Z. (2015). Adaptive fuzzy finite-time control for a class of switched nonlinear systems with unknown control coefficients. Neurocomputing, 162, 105–115. https://doi.org/10.1016/j.neucom.2015.03.064
   Web of Science ®Google Scholar
• Dai, S. L., He, S., Wang, M., & Yuan, C. (2019). Adaptive neural control of underactuated surface vessels with prescribed performance guarantees. IEEE Transactions on Neural Networks and Learning Systems, 30(12), 3686–3698. https://doi.org/10.1109/TNNLS.5962385
   PubMed Web of Science ®Google Scholar
• Dai, S. L., Lu, K., & Fu, J. (2021). Adaptive finite-time tracking control of nonholonomic multirobot formation systems with limited field-of-view sensors. IEEE Transactions on Cybernetics. https://doi.org/10.1109/TCYB.2021.3063481
   Web of Science ®Google Scholar
• Dai, S. L., Wang, C., & Wang, M. (2014). Dynamic learning from adaptive neural network control of a class of nonaffine nonlinear systems. IEEE Transactions on Neural Networks and Learning Systems, 25(1), 111–123. https://doi.org/10.1109/TNNLS.2013.2257843
   PubMed Web of Science ®Google Scholar
• Farhat, Y., Zribi, A., Atig, A., & Abdennour, R. B. (2022). A neural multicontroller for strongly nonlinear systems. International Journal of Systems Science, 53(8), 1778–1795. https://doi.org/10.1080/00207721.2021.2024295
   Web of Science ®Google Scholar
• Fu, J., Ma, R., & Chai, T. (2015). Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers. Automatica, 54(4), 360–373. https://doi.org/10.1016/j.automatica.2015.02.023
   Web of Science ®Google Scholar
• Fu, J., Ma, R., & Chai, T. (2017). Adaptive finite-time stabilization of a class of uncertain nonlinear systems via logic-based switchings. IEEE Transactions on Automatic Control, 62(11), 5998–6003. https://doi.org/10.1109/TAC.2017.2705287
   Web of Science ®Google Scholar
• Fu, Z., Wang, N., Song, S., & Wang, T. (2022). Adaptive fuzzy finite-time tracking control of stochastic high-order nonlinear systems with a class of prescribed performance. IEEE Transactions on Fuzzy Systems, 30(1), 88–96. https://doi.org/10.1109/TFUZZ.2020.3032776
   Web of Science ®Google Scholar
• Gao, H., Lam, J., Wang, C., & Xu, S. (2005). Control for stability and positivity: Equivalent conditions and computation. IEEE Transactions on Circuits and Systems II: Express Briefs, 52(9), 540–544. https://doi.org/10.1109/TCSII.2005.850525
   Web of Science ®Google Scholar
• Ghazisaeedi, H. R., & Tavazoei, M. S. (2022). Finite-time stabilisation of a class of time-varying nonlinear systems by a mixed event-based and continuous-time strategy. International Journal of Systems Science, 53(3), 526–537. https://doi.org/10.1080/00207721.2021.1963006
   Web of Science ®Google Scholar
• He, S., Dong, C., Dai, S. L., & Zou, T. (2022). Cooperative deterministic learning and formation control for underactuated usvs with prescribed performance. International Journal of Robust and Nonlinear Control, 32(5), 2902–2924. https://doi.org/10.1002/rnc.v32.5
   Web of Science ®Google Scholar
• He, X., Li, X., & Nieto, J. J. (2021). Finite-time stability and stabilization for time-varying systems. Chaos, Solitons and Fractals, 148, Article ID 111076. https://doi.org/10.1016/j.chaos.2021.111076
   Web of Science ®Google Scholar
• He, X., Li, X., & Song, S. (2022). Finite-time input-to-state stability of nonlinear impulsive systems. Automatica, 135, Article ID 109994. https://doi.org/10.1016/j.automatica.2021.109994
   Web of Science ®Google Scholar
• Hu, T., Lin, Z., & Chen, B. M. (2002). An analysis and design method for linear systems subject to actuator saturation and disturbance. Automatica, 38(2), 351–359. https://doi.org/10.1016/S0005-1098(01)00209-6
   Web of Science ®Google Scholar
• Huang, S., Yan, Z., Zeng, G., Zhang, Z., & Zhu, Z. (2021). Finite-time prescribed performance control of switched nonlinear systems with input quantisation. International Journal of Systems Science, 52(4), 857–873. https://doi.org/10.1080/00207721.2020.1849858
   Web of Science ®Google Scholar
• Huang, X., Lin, W., & Yang, B. (2005). Global finite-time stabilization of a class of uncertain nonlinear systems. Automatica, 41(5), 881–888. https://doi.org/10.1016/j.automatica.2004.11.036
   Web of Science ®Google Scholar
• Huo, X., Karimi, H. R., Zhao, X., Wang, B., & Zong, G. (2022). Adaptive-critic design for decentralized event-triggered control of constrained nonlinear interconnected systems within an identifier-critic framework. IEEE Transactions on Cybernetics, 52(8), 7478–7491. https://doi.org/10.1109/TCYB.2020.3037321
   PubMed Web of Science ®Google Scholar
• Jiang, T., & Lin, D. (2020). Fast finite-time backstepping for helicopters under input constraints and perturbations. International Journal of Systems Science, 51(15), 2868–2882. https://doi.org/10.1080/00207721.2020.1803438
   Web of Science ®Google Scholar
• Jiao, T., Zhang, C., Ma, Q., Zong, G., & Wang, Y. (2017). Stability analysis of a class of random nonlinear time-varying systems. In 2017 36th Chinese control conference (CCC) (pp. 1713–1716). IEEE.
   Google Scholar
• Krishnamurthy, P., Khorrami, F., & Krstic, M. (2020). A dynamic high-gain design for prescribed-time regulation of nonlinear systems. Automatica, 115, Article ID 108860. https://doi.org/10.1016/j.automatica.2020.108860
   Web of Science ®Google Scholar
• Li, X., & Peng, D. (2022). Uniform stability of nonlinear systems with state-dependent delay. Automatica, 137, Article ID 110098. https://doi.org/10.1016/j.automatica.2021.110098
   PubMed Web of Science ®Google Scholar
• Lian, Z., Shi, P., & Lim, C. C. (2021). Dynamic hybrid-triggered-based fuzzy control for nonlinear networks under multiple cyber-attacks. IEEE Transactions on Fuzzy Systems. https://doi.org/10.1109/TFUZZ.2021.3134745
   Web of Science ®Google Scholar
• Liang, Y. J., Ma, R., Wang, M., & Fu, J. (2015). Global finite-time stabilisation of a class of switched nonlinear systems. International Journal of Systems Science, 46(16), 2897–2904. https://doi.org/10.1080/00207721.2014.880197
   Web of Science ®Google Scholar
• Liu, B., Hou, M., Wu, C., Wang, W., Wu, Z., & Huang, B. (2021). Predefined-time backstepping control for a nonlinear strict-feedback system. International Journal of Robust and Nonlinear Control, 31(8), 3354–3372. https://doi.org/10.1002/rnc.v31.8
   Web of Science ®Google Scholar
• Liu, W., & Zhou, C. (2021). Fault-tolerant finite-time fuzzy control for nonlinear power systems with time delays and actuator faults. ISA Transactions, 118, 44–54. https://doi.org/10.1016/j.isatra.2021.02.008
   PubMed Web of Science ®Google Scholar
• Liu, X., & Lin, Z. (2011). On normal forms of nonlinear systems affine in control. IEEE Transactions on Automatic Control, 56(2), 239–253. https://doi.org/10.1109/TAC.2010.2051634
   Web of Science ®Google Scholar
• Liu, Y., & Zhu, Q. (2022). Adaptive fuzzy asymptotic control for switched nonlinear systems with state constraints. International Journal of Systems Science, 53(5), 922–933. https://doi.org/10.1080/00207721.2021.1979684
   Web of Science ®Google Scholar
• Lopez-Ramirez, F., Polyakov, A., Efimov, D., & Perruquetti, W. (2018). Finite-time and fixed-time observer design: Implicit lyapunov function approach. Automatica, 87, 52–60. https://doi.org/10.1016/j.automatica.2017.09.007
   Web of Science ®Google Scholar
• Moulay, E., & Perruquetti, W. (2006). Finite-time stability and stabilization: State of the art. Lecture Notes in Control and Information Science, 334, 23–41. https://doi.org/10.1007/11612735
   Google Scholar
• Ngo, K. B., Mahony, R., & Jiang, Z. P. (2005). Integrator backstepping using barrier functions for systems with multiple state constraints. In 44th IEEE conference on 2005 decision and control, 2005 and 2005 European control conference. CDC-ECC '05 (pp. 8306–8312). IEEE.
   Google Scholar
• Noori Skandari, M., Ghaznavi, M., & Abedian, M. (2019). Stabilizer control design for nonlinear systems based on the hyperbolic modelling. Applied Mathematical Modelling, 67, 413–429. https://doi.org/10.1016/j.apm.2018.11.006
   Web of Science ®Google Scholar
• Polyakov, A. (2012). Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Transactions on Automatic Control, 57(8), 2106–2110. https://doi.org/10.1109/TAC.2011.2179869
   Web of Science ®Google Scholar
• Polyakov, A., Efimov, D., & Perruquetti, W. (2015). Finite-time and fixed-time stabilization: Implicit lyapunov function approach. Automatica, 51, 332–340. https://doi.org/10.1016/j.automatica.2014.10.082
   Web of Science ®Google Scholar
• Pourdehi, S., & Karimaghaee, P. (2018). Stability analysis and design of model predictive reset control for nonlinear time-delay systems with application to a two-stage chemical reactor system. Journal of Process Control, 71, 103–115. https://doi.org/10.1016/j.jprocont.2018.09.010
   Web of Science ®Google Scholar
• Shen, Y., & Huang, Y. (2012). Global finite-time stabilisation for a class of nonlinear systems. International Journal of Systems Science, 43(1), 73–78. https://doi.org/10.1080/00207721003770569
   Web of Science ®Google Scholar
• Song, Y., Wang, Y., Holloway, J., & Krstic, M. (2017). Time-varying feedback for regulation of normal-form nonlinear systems in prescribed finite time. Automatica, 83, 243–251. https://doi.org/10.1016/j.automatica.2017.06.008
   Web of Science ®Google Scholar
• Song, Z., & Li, P. (2021). Fixed-time stabilisation for switched stochastic nonlinear systems with asymmetric output constraints. International Journal of Systems Science, 52(5), 990–1002. https://doi.org/10.1080/00207721.2020.1852625
   Web of Science ®Google Scholar
• Sun, Z. Y., Li, T., & Yang, S. H. (2016). A unified time-varying feedback approach and its applications in adaptive stabilization of high-order uncertain nonlinear systems. Automatica, 70, 249–257. https://doi.org/10.1016/j.automatica.2016.04.010
   Web of Science ®Google Scholar
• Tee, K. P., & Ge, S. S. (2012). Control of state-constrained nonlinear systems using integral barrier lyapunov functionals. In 2012 IEEE 51st IEEE conference on decision and control (CDC) (pp. 3239–3244). IEEE.
   Google Scholar
• Wang, L., Ortega, R., Su, H., & Liu, Z. (2015). Stabilization of nonlinear systems nonlinearly depending on fast time-varying parameters: An immersion and invariance approach. IEEE Transactions on Automatic Control, 60(2), 559–564. https://doi.org/10.1109/TAC.2014.2345272
   Web of Science ®Google Scholar
• Wang, M., Wang, L., & Yang, C. (2021). Sliding mode differentiator-based event-triggered control for state-constrained nonlinear systems with unknown virtual control coefficients. International Journal of Control. https://doi.org/10.1080/00207179.2021.2005828
   Web of Science ®Google Scholar
• Wang, M., Wang, Z., Dong, H., & Han, Q. L. (2021). A novel framework for backstepping-based control of discrete-time strict-feedback nonlinear systems with multiplicative noises. IEEE Transactions on Automatic Control, 66(4), 1484–1496. https://doi.org/10.1109/TAC.2020.2995576
   Web of Science ®Google Scholar
• Wang, N., Fu, Z., Song, S., & Wang, T. (2022). Barrier-lyapunov-based adaptive fuzzy finite-time tracking of pure-feedback nonlinear systems with constraints. IEEE Transactions on Fuzzy Systems, 30(4), 1139–1148. https://doi.org/10.1109/TFUZZ.2021.3053322
   Web of Science ®Google Scholar
• Wen, G., Ge, S. S., & Tu, F. (2018). Optimized backstepping for tracking control of strict-feedback systems. IEEE Transactions on Neural Networks and Learning Systems, 29(8), 3850–3862. https://doi.org/10.1109/TNNLS.2018.2803726
   PubMed Web of Science ®Google Scholar
• Wu, B., & Ding, Z. (2009). Asymptotic stabilisation of a class of nonlinear systems via sampled-data output feedback control. International Journal of Control, 82(9), 1738–1746. https://doi.org/10.1080/00207170902725615
   Web of Science ®Google Scholar
• Xu, N., Chen, Y., Xue, A., & Zong, G. (2022). Finite-time stabilization of continuous-time switched positive delayed systems. Journal of the Franklin Institute, 359(1), 255–271. https://doi.org/10.1016/j.jfranklin.2021.04.022
   Web of Science ®Google Scholar
• Yu, J., Shi, P., & Zhao, L. (2018). Finite-time command filtered backstepping control for a class of nonlinear systems. Automatica, 92, 173–180. https://doi.org/10.1016/j.automatica.2018.03.033
   Web of Science ®Google Scholar
• Zhang, K., & Zhang, X. H. (2015). Finite-time stabilisation for high-order nonlinear systems with low-order and high-order nonlinearities. International Journal of Control, 88(8), 1576–1585. https://doi.org/10.1080/00207179.2015.1011697
   Web of Science ®Google Scholar
• Zhou, B., & Shi, Y. (2021). Prescribed-time stabilization of a class of nonlinear systems by linear time-varying feedback. IEEE Transactions on Automatic Control, 66(12), 6123–6130. https://doi.org/10.1109/TAC.2021.3061645
   Web of Science ®Google Scholar