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Research Articles

Real-time reachable set estimation for linear time-delay systems based on zonotopes

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Pages 1639-1647 | Received 26 Oct 2022, Accepted 26 Feb 2023, Published online: 19 Apr 2023

References

  • Alamo, T., Bravo, J. M., & Camacho, E. F. (2005). Guaranteed state estimation by zonotopes. Automatica, 41(6), 1035–1043. https://doi.org/10.1016/j.automatica.2004.12.008
  • Althoff, M., Frehse, G., & Girard, A. (2021). Set propagation techniques for reachability analysis. Annual Review of Control, Robotics, and Autonomous Systems, 4(1), 369–395. https://doi.org/10.1146/control.2021.4.issue-1
  • Althoff, M., Stursberg, O., & Buss, M. (2010). Computing reachable sets of hybrid systems using a combination of zonotopes and polytopes. Nonlinear Analysis: Hybrid Systems, 4(2), 233–249. https://doi.org/10.1016/j.nahs.2009.03.009.
  • Bravo, J. M., Alamo, T., & Camacho, E. F. (2006). Robust MPC of constrained discrete-time nonlinear systems based on approximated reachable sets. Automatica, 42(10), 1745–1751. https://doi.org/10.1016/j.automatica.2006.05.003
  • Chen, Y., Lam, J., & Zhang, B. (2016). Estimation and synthesis of reachable set for switched linear systems. Automatica, 63, 122–132. https://doi.org/10.1016/j.automatica.2015.10.033
  • Chutinan, A., & Krogh, B. H. (2003). Computational techniques for hybrid system verification. IEEE Transactions on Automatic Control, 48(1), 64–75. https://doi.org/10.1109/TAC.2002.806655
  • Combastel, C. (2005). A state bounding observer for uncertain non-linear continuous-time systems based on zonotopes. In Proceeding of the 44th IEEE Conference on Decision and Control (pp. 7228–7234). IEEE.
  • Combastel, C. (2015). Zonotopes and Kalman observers: Gain optimality under distinct uncertainty paradigms and robust convergence. Automatica, 55, 265–273. https://doi.org/10.1016/j.automatica.2015.03.008
  • Durieu, C., Polyak, B. T., & Walter, E. (1996). Trace versus determinant in ellipsoidal outer-bounding, with application to state estimation. In Proceedings of the 13th World Congress of International Federation of Automatic Control (Vol. 29, pp. 3975–3980).
  • Fei, Z., Guan, C., & Shi, P. (2018). Reachable set estimation for discrete-time switched system with application to time-delay system. International Journal of Robust and Nonlinear Control, 28(6), 2468–2483. https://doi.org/10.1002/rnc.v28.6
  • Feng, Z., & Lam, J. (2015). On reachable set estimation of singular systems. Automatica, 52, 146–153. https://doi.org/10.1016/j.automatica.2014.11.007
  • Feng, Z., Zheng, W. X., & Wu, L. (2017). Reachable set estimation of T-S fuzzy systems with time-varying delay. IEEE Transactions on Fuzzy Systems, 25(4), 878–891. https://doi.org/10.1109/TFUZZ.2016.2586945
  • Fridman, E., & Shaked, U. (2003). On reachable sets for linear systems with delay and bounded peak inputs. Automatica, 39(11), 2005–2010. https://doi.org/10.1016/S0005-1098(03)00204-8
  • Guo, S., Ren, W., Ahn, C. K., Wen, C., & Lam, H. K. (2021). Reachability analysis-based interval estimation for discrete-time Takagi–Sugeno fuzzy systems. IEEE Transactions on Fuzzy Systems, 30(6), 1981–1992. https://doi.org/10.1109/TFUZZ.2021.3072681
  • Kurzhanski, A. A., & Varaiya, P. (2007). Ellipsoidal techniques for reachability analysis of discrete-time linear systems. IEEE Transactions on Automatic Control, 52(1), 26–38. https://doi.org/10.1109/TAC.2006.887900
  • Lam, L., Zhang, B. Y., Chen, Y., & Xu, S. Y. (2015). Reachable set estimation for discrete-time linear systems with time delays. International Journal of Robust and Nonlinear Control, 25(2), 269–281. https://doi.org/10.1002/rnc.3086
  • Le, V. T. H., Maniu, C. S., Alamo, T., Camacho, E. F., & Dumur, D. (2010). Zonotopes: From guaranteed state-estimation to control. John Wiley & Sons, Inc.
  • Li, J., Wang, Z., Shen, Y., & Wang, Y. (2018). Zonotopic fault detection observer design for Takagi-Sugeno fuzzy systems. International Journal of Systems Science, 49(15), 3216–3230. https://doi.org/10.1080/00207721.2018.1535101
  • Li, J., Wang, Z., Shen, Y., & Xie, L. (2022). A zonotopic characterization of cyber-physical system vulnerabilities. International Journal of Robust and Nonlinear Control, 32(9), 5379–5397. https://doi.org/10.1002/rnc.v32.9
  • Liu, H., Niu, B., & Qin, J. (2019). Reachability analysis for linear discrete-time systems under stealthy cyber attacks. IEEE Transactions on Automatic Control, 66(9), 4444–4451. https://doi.org/10.1109/TAC.2021.3050549
  • Ping, X., Yang, S., Xiao, Y., Ding, B., & Li, Z. (2021). Interval state estimation-based robust model predictive control for linear parameter varying systems. International Journal of Robust and Nonlinear Control, 31(15), 7026–7052. https://doi.org/10.1002/rnc.v31.15
  • Scott, J. K., Raimondo, D. M., Marseglia, G. R., & Braatz, R. D. (2016). Constrained zonotopes: A new tool for set-based estimation and fault detection. Automatica, 69, 126–136. https://doi.org/10.1016/j.automatica.2016.02.036
  • Shephard, G. C. (1974). Combinatorial properties of associated zonotopes. Canadian Journal of Mathematics, 26(2), 302–321. https://doi.org/10.4153/CJM-1974-032-5
  • Tan, J., Xu, F., Wang, X., Yang, J., & Liang, B. (2019). Invariant set-based robust fault detection and optimal fault estimation for discrete-time LPV systems with bounded uncertainties. International Journal of Systems Science, 50(16), 2962–2978. https://doi.org/10.1080/00207721.2019.1691283
  • Tang, W., Wang, Z., Raïssi, T., Wang, Y., & Shen, Y. (2019). Interval estimation methods for discrete-time linear time-invariant systems. IEEE Transactions on Automatic Control, 64(11), 4717–4724. https://doi.org/10.1109/TAC.9
  • Tang, W., Wang, Z., & Shen, Y. (2020). Fault detection and isolation for discrete-time descriptor systems based on H−/L∞ observer and zonotopic residual evaluation. International Journal of Control, 93(8), 1867–1878. https://doi.org/10.1080/00207179.2018.1535716
  • Tang, W., Zhang, Q., Wang, Z., & Shen, Y. (2022). Set-membership estimation based on ellipsoid bundles for discrete-time LPV descriptor systems. Automatica, 145, Article 110580. https://doi.org/10.1016/j.automatica.2022.110580
  • Wang, Y., Wang, Z., Raïssi, T., Puig, V., & Cembrano, G. (2018). Zonotopic set-membership state estimation for discrete-time descriptor LPV systems. IEEE Transactions on Automatic Control, 64(5), 2092–2099. https://doi.org/10.1109/TAC.9
  • Wang, Z., Dinh, T. N., Zhang, Q., Raïssi, T., & Shen, Y. (2022). Fast interval estimation for discrete-time linear systems: An L1 optimization method. Automatica, 137, Article 110029. https://doi.org/10.1016/j.automatica.2021.110029.
  • Wang, Z., Lim, C. C., & Shen, Y. (2018). Interval observer design for uncertain discrete-time linear systems. Systems & Control Letters, 116, 4717–4724. https://doi.org/10.1016/j.sysconle.2018.04.003
  • Xu, F., Tan, J., Wang, Y., Wang, X., Liang, B., & Yuan, B. (2019). Robust fault detection and set-theoretic UIO for discrete-time LPV systems with state and output equations scheduled by inexact scheduling variables. IEEE Transactions on Automatic Control, 64(12), 4982–4997. https://doi.org/10.1109/TAC.9
  • Zhang, W., Wang, Z., Raïssi, T., & Shen, Y. (2021). Ellipsoid-based interval estimation for Lipschitz nonlinear systems. IEEE Transactions on Automatic Control, 67(12), 6802–6809. https://doi.org/10.1109/TAC.2021.3133366
  • Zhang, Z., & Feng, Z. (2021). Enclosing ellipsoid-based reachable set estimation for discrete-time singular systems. International Journal of Robust and Nonlinear Control, 32(17), 9294–9306. https://doi.org/10.1002/rnc.v32.17
  • Zhang, Z., Wang, Z., Tang, W., Feng, Z., & Shen, Y. (2020). Zonotopic reachable set estimation for linear discrete-time systems with time delay. International Journal of Robust and Nonlinear Control, 30(14), 5542–5558. https://doi.org/10.1002/rnc.v30.14
  • Zhang, Z., Wang, Z., Wang, Y., Shen, Y., & Liu, Y. (2021). Zonotopic reachable set estimation for bilinear systems with time-varying delays. International Journal of Systems Science, 52(4), 848–856. https://doi.org/10.1080/00207721.2020.1849857
  • Zhao, Z., Wang, Z., & Zou, L. (2022). Sequential fusion estimation for multirate complex networks with uniform quantization: A Zonotopic set-membership approach. IEEE Transactions on Neural Networks and Learning Systems, 1–14. https://doi.org/10.1109/TNNLS.2022.3209135
  • Zhao, Z., Wang, Z., Zou, L., Liu, H., & Alsaadi, F. E. (2023). Zonotopic multi-sensor fusion estimation with mixed delays under try-once-discard protocol: A set-membership framework. Information Fusion, 91, 681–693. https://doi.org/10.1016/j.inffus.2022.11.012
  • Zuo, Z., Ho, D. W. C., & Wang, Y. (2010). Reachable set bounding for delayed systems with polytopic uncertainties: The maximal Lyapunov-Krasovskii functional approach. Automatica, 46(5), 949–952. https://doi.org/10.1016/j.automatica.2010.02.022

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