Fixed-time boundary stabilisation for delay reaction–diffusion systems

References

• Adomian, G. (1997). On the dynamics of a reaction–diffusion system. Applied Mathematics and Computation, 8(1), 193–195. https://doi.org/10.1016/0096-3003(95)00312-6
   Web of Science ®Google Scholar
• Andrieu, V., Praly, L., & Astolfi, A. (2008). Homogeneous approximation, recursive observer design, and output feedback. SIAM Journal on Control and Optimization, 47(4), 1814–1850. https://doi.org/10.1137/060675861
   Web of Science ®Google Scholar
• Aouiti, C., & Jallouli, H. (2021). State feedback controllers based finite-time and fixed-time stabilisation of high order BAMs with reaction–diffusion term. International Journal of Systems Science, 52(5), 905–927. https://doi.org/10.1080/00207721.2020.1849861
   Web of Science ®Google Scholar
• Ba, D., Li, Y. X., & Tong, S. (2019). Fixed-time adaptive neural tracking control for a class of uncertain nonstrict nonlinear systems. Neurocomputing, 363(21), 273–280. https://doi.org/10.1016/j.neucom.2019.06.063
   Web of Science ®Google Scholar
• Bhat, S., & Bernstein, D. (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
• Boyd, S., El Ghaoui, L., Feron, E., & Balakrishnan, V. (1994). Linear matrix inequalities in system and control theory. Society for Industrial and Applied Mathematics (SIAM).
   Google Scholar
• Chen, G., Xia, J., & Zhuang, G. (2016). Delay-dependent stability and dissipativity analysis of generalized neural networks with Markovian jump parameters and two delay components. Journal of The Franklin Institute-Engineering and Applied Mathematics, 353(9), 2137–2158. https://doi.org/10.1016/j.jfranklin.2016.02.020
   Web of Science ®Google Scholar
• Cruz-Zavala, E., Moreno, J. A., & Fridman, L. M. (2011). Uniform robust exact differentiator. IEEE Transactions on Automatic Control, 56(11), 2727–2733. https://doi.org/10.1109/TAC.2011.2160030
   Web of Science ®Google Scholar
• Du, H., Zhang, J., Wu, D., Zhu, W., Li, H., & Chu, Z. (2019). Fixed-time attitude stabilization for a rigid spacecraft. ISA Transactions, 98, 263–270. https://doi.org/10.1016/j.isatra.2019.08.026
   PubMed Web of Science ®Google Scholar
• Duan, L., Shi, M., Huang, C., & Fang, X. (2021). Synchronization in finite-/fixed-time of delayed diffusive complex-valued neural networks with discontinuous activations. Chaos, Solitons & Fractals, 142, Article 110386. https://doi.org/10.1016/j.chaos.2020.110386
   Web of Science ®Google Scholar
• Duan, L., Shi, M., & Huang, L. (2021). New results on finite-/fixed-time synchronization of delayed diffusive fuzzy HNNs with discontinuous activations. Fuzzy Sets and Systems, 416, 141–151. https://doi.org/10.1016/j.fss.2020.04.016
   Web of Science ®Google Scholar
• Espitia, N., Polyakov, A., Efimov, D., & Perruquetti, W. (2019a). Boundary time-varying feedbacks for fixed-time stabilization of constant-parameter reaction–diffusion systems. Automatica, 103, 398–407. https://doi.org/10.1016/j.automatica.2019.02.013
   Web of Science ®Google Scholar
• Espitia, N., Polyakov, A., Efimov, D., & Perruquetti, W. (2019b). Some characterizations of boundary time-varying feedbacks for fixed-time stabilization of reaction–diffusion systems. IFAC-PapersOnLine, 52(2), 162–167. https://doi.org/10.1016/j.ifacol.2019.08.029
   Google Scholar
• Grindrod, P. (1996, January). The theory and applications of reaction–diffusion equations. Oxford.
   Google Scholar
• Guin, L. N., & Acharya, S. (2017). Dynamic behaviour of a reaction–diffusion predator–prey model with both refuge and harvesting. Nonlinear Dynamics, 88(2), 1501–1533. https://doi.org/10.1007/s11071-016-3326-8
   Web of Science ®Google Scholar
• Haimo, V. (1986). Finite-time controllers. SIAM Journal on Control and Optimization, 24(4), 760–770. https://doi.org/10.1137/0324047
   Web of Science ®Google Scholar
• Horváth, J., Szalai, I., & Kepper, P. D. (2018). Designing stationary reaction–diffusion patterns in pH self-activated systems. Accounts of Chemical Research, 51(12), 3183–3190. https://doi.org/10.1021/acs.accounts.8b00441
   PubMed Web of Science ®Google Scholar
• Hu, C., Yu, J., Chen, Z., Jiang, H., & Huang, T. (2017). Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks. Neural Networks, 89, 74–83. https://doi.org/10.1016/j.neunet.2017.02.001
   PubMed Web of Science ®Google Scholar
• Hu, J., & Sui, G. (2019). Fixed-time control of static impulsive neural networks with infinite distributed delay and uncertainty. Communications in Nonlinear Science and Numerical Simulation, 78, Article 104848. https://doi.org/10.1016/j.cnsns.2019.05.006
   Web of Science ®Google Scholar
• Huang, C. H., & Li, C. Y. (2003). A three-dimensional optimal control problem in determining the boundary control heat fluxes. Heat and Mass Transfer, 39(7), 589–598. https://doi.org/10.1007/s00231-002-0314-y
   Web of Science ®Google Scholar
• Jiang, M. M., & Xie, X. J. (2018). Adaptive finite-time stabilisation of high-order uncertain nonlinear systems. International Journal of Control, 91(10), 2159–2169. https://doi.org/10.1080/00207179.2016.1245869
   Web of Science ®Google Scholar
• Kao, Y., Shao, C., & Chen, X. (2021). Stability of high-order delayed Markovian jumping reaction–diffusion HNNs with uncertain transition rates. Applied Mathematics and Computation, 389, Article 125559. https://doi.org/10.1016/j.amc.2020.125559
   Web of Science ®Google Scholar
• Lhachemi, H., Prieur, C., & Shorten, R. (2021). Robustness of constant-delay predictor feedback for in-domain stabilization of reaction–diffusion PDEs with time and spatially-varying input delays. Automatica, 123, Article 109347. https://doi.org/10.1016/j.automatica.2020.109347
   Web of Science ®Google Scholar
• Li, M., Jiang, M., Ren, F., & Zhang, Y. (2021). Finite-time stability of a class of nonautonomous systems. International Journal of Control, 95(10), 2771–2779. https://doi.org/10.1080/00207179.2021.1934735
   Web of Science ®Google Scholar
• Lin, Y., Liu, Y., & Li, Z. (2013). Exact solutions for pattern formation in a reaction–diffusion system. International Journal of Nonlinear Sciences and Numerical Simulation, 14(5), 307–315. https://doi.org/10.1515/ijnsns-2012-0167
   Web of Science ®Google Scholar
• Liu, L., Xu, S., & Zhang, Y. (2017). Finite-time output feedback control for a class of stochastic low-order nonlinear systems. International Journal of Control, 90(7), 1457–1465. https://doi.org/10.1080/00207179.2016.1209563
   Web of Science ®Google Scholar
• Liu, X., & Liao, X. (2019a). Fixed-time H∞ control for port-controlled Hamiltonian systems. IEEE Transactions on Automatic Control, 64(7), 2753–2765. https://doi.org/10.1109/TAC.9
   Web of Science ®Google Scholar
• Liu, X., & Liao, X. (2019b). Fixed-time stabilization control for port-Hamiltonian systems. Nonlinear Dynamics, 96(2), 1497–1509. https://doi.org/10.1007/s11071-019-04867-0
   Web of Science ®Google Scholar
• Liu, X. Z., Li, Z. T., & Wu, K. N. (2020). Boundary Mittag-Leffler stabilization of fractional reaction–diffusion cellular neural networks. Neural Networks, 132, 269–280. https://doi.org/10.1016/j.neunet.2020.09.009
   PubMed Web of Science ®Google Scholar
• Liu, X. Z., Wu, K. N., & Li, Z. T. (2021). Exponential stabilization of reaction–diffusion systems via intermittent boundary control. IEEE Transactions on Automatic Control, 67(6), 3036–3042. https://doi.org/10.1109/TAC.2021.3100289
   Web of Science ®Google Scholar
• Liu, Y., & Yang, G. H. (2019). Fixed-time fault-tolerant consensus control for multi-agent systems with mismatched disturbances. Neurocomputing, 366, 154–160. https://doi.org/10.1016/j.neucom.2019.07.093
   Web of Science ®Google Scholar
• Lopez-Ramirez, F., Efimov, D., Polyakov, A., & Perruquetti, W. (2019). Conditions for fixed-time stability and stabilization of continuous autonomous systems. Systems & Control Letters, 129, 26–35. https://doi.org/10.1016/j.sysconle.2019.05.003
   Web of Science ®Google Scholar
• Matsunaga, T., Uemura, R., & Hori, Y. (2021). Finite-time stability analysis for resource limited chemical reactions. IEEE Control Systems Letters, 5(3), 815–820. https://doi.org/10.1109/LCSYS.7782633
   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
• Tucsnak, M., & Weiss, G. (2009). Observation and control for operator semigroups. Birkhäuser Basel.
   Google Scholar
• Wang, J. L., & Wu, H. N. (2013). Passivity of delayed reaction–diffusion networks with application to a food web model. Applied Mathematics and Computation, 219(24), 11311–11326. https://doi.org/10.1016/j.amc.2013.04.059
   Web of Science ®Google Scholar
• Wang, Z., Cao, J., Lu, G., & Abdel-Aty, M. (2020). Fixed-time passification analysis of interconnected memristive reaction–diffusion neural networks. IEEE Transactions on Network Science and Engineering, 7(3), 1814–1824. https://doi.org/10.1109/TNSE.6488902
   Web of Science ®Google Scholar
• Wen, L., Yu, S., Zhao, Y., & Yan, Y. (2021). Finite-time dynamic event-triggered consensus of multi-agent systems with disturbances via integral sliding mode. International Journal of Control, 95(10), 2771–2779. https://doi.org/10.1080/00207179.2021.1989045
   Web of Science ®Google Scholar
• Wu, H. N., Wang, J. W., & Li, H. X. (2014). Fuzzy boundary control design for a class of nonlinear parabolic distributed parameter systems. IEEE Transactions on Fuzzy Systems, 22(3), 642–652. https://doi.org/10.1109/TFUZZ.91
   Web of Science ®Google Scholar
• Wu, K. N., Liu, X. Z., Yang, B., & Lim, C. C. (2019). Mean square finite-time synchronization of impulsive stochastic delay reaction–diffusion systems. Communications in Nonlinear Science and Numerical Simulation, 79, Article 104899. https://doi.org/10.1016/j.cnsns.2019.104899
   Web of Science ®Google Scholar
• Wu, K. N., Na, M. Y., Wang, L., Ding, X., & Wu, B. (2019). Finite-time stability of impulsive reaction–diffusion systems with and without time delay. Applied Mathematics and Computation, 363, Article 124591. https://doi.org/10.1016/j.amc.2019.124591
   Web of Science ®Google Scholar
• Wu, K. N., Sun, H. X., Shi, P., & Lim, C. C. (2017). Finite-time boundary stabilization of reaction–diffusion systems. International Journal of Robust and Nonlinear Control, 28(5), 1641–1652. https://doi.org/10.1002/rnc.v28.5
   Web of Science ®Google Scholar
• Wu, K. N., Sun, H. X., Yang, B., & Lim, C. C. (2018). Finite-time boundary control for delay reaction–diffusion systems. Applied Mathematics and Computation, 329, 52–63. https://doi.org/10.1016/j.amc.2018.01.048
   Web of Science ®Google Scholar
• Wu, K. N., Wang, J., & Lim, C. C. (2018, June). Synchronization of stochastic reaction–diffusion systems via boundary control. Nonlinear Dynamics, 94(3), 1763–1773. https://doi.org/10.1007/s11071-018-4455-z
   Web of Science ®Google Scholar
• Xia, J., Chen, G., & Sun, W. (2017). Extended dissipative analysis of generalized Markovian switching neural networks with two delay components. Neurocomputing, 260, 275–283. https://doi.org/10.1016/j.neucom.2017.05.005
   Web of Science ®Google Scholar
• Yan, Z., Park, J. H., & Zhang, W. (2016). Finite-time guaranteed cost control for Itô stochastic Markovian jump systems with incomplete transition rates. International Journal of Robust and Nonlinear Control, 27(1), 66–83. https://doi.org/10.1002/rnc.v27.1
   Web of Science ®Google Scholar
• Yan, Z., Song, Y., & Park, J. H. (2017). Finite-time stability and stabilization for stochastic Markov jump systems with mode-dependent time delays. ISA Transactions, 68, 141–149. https://doi.org/10.1016/j.isatra.2017.01.018
   PubMed Web of Science ®Google Scholar
• Yao, Q., Wang, L., & Wang, Y. (2019). Periodic solutions to impulsive stochastic reaction–diffusion neural networks with delays. Communications in Nonlinear Science and Numerical Simulation, 78, Article 104865. https://doi.org/10.1016/j.cnsns.2019.104865
   Web of Science ®Google Scholar
• Zhang, J., Chadli, M., & Wang, Y. (2019). A fixed-time observer for discrete-time singular systems with unknown inputs. Applied Mathematics and Computation, 363, Article 124586. https://doi.org/10.1016/j.amc.2019.124586
   Web of Science ®Google Scholar
• Zhang, J., & Efimov, D. (2021). Fixed-time and finite-time stability of switched time-delay systems. International Journal of Control, 95(10), 2780–2792. https://doi.org/10.1080/00207179.2021.1934736
   Web of Science ®Google Scholar
• Zhang, L., Wei, C., Jing, L., & Cui, N. (2018). Fixed-time sliding mode attitude tracking control for a submarine-launched missile with multiple disturbances. Nonlinear Dynamics, 93(4), 2543–2563. https://doi.org/10.1007/s11071-018-4341-8
   Web of Science ®Google Scholar
• Zhou, J., Zhang, Y., Chen, J. K., & Feng, Z. C. (2010). Inverse estimation of spatially and temporally varying heating boundary conditions of a two-dimensional object. International Journal of Thermal Sciences, 49(9), 1669–1679. https://doi.org/10.1016/j.ijthermalsci.2010.04.009
   Web of Science ®Google Scholar
• Zhou, Y., Yu, X., Sun, C., & Yu, W. (2015). Higher order finite-time consensus protocol for heterogeneous multi-agent systems. International Journal of Control, 88(2), 285–294. https://doi.org/10.1080/00207179.2014.950047
   Web of Science ®Google Scholar