Spatiotemporally asynchronous sampled-data control of a linear parabolic PDE on a hypercube

References

• Bar Am, N., & Fridman, E. (2014). Network-based H∞ filtering of parabolic systems. Automatica, 50(12), 3139–3146. https://doi.org/10.1016/j.automatica.2014.10.009
   Web of Science ®Google Scholar
• Chen, T., & Francis, B. (1996). Optimal sampled-data control systems (2nd ed.). Springer-Verlag.
   Google Scholar
• Chen, W.-H., Luo, S., & Zheng, W.-X. (2017). Sampled-data distributed H∞ control of a class of 1-D parabolic systems under spatially point measurements. Journal of the Franklin Institute, 354(1), 197–214. https://doi.org/10.1016/j.jfranklin.2016.09.028
   Web of Science ®Google Scholar
• Cheng, M.-B., Radisavljevic, V., Chang, C.-C., Lin, C. F., & Su, W. C. (2009). A sampled-data singularly perturbed boundary control for a heat conduction system with noncollocated observation. IEEE Transactions on Automatic Control, 54(5), 1305–1310. https://doi.org/10.1109/TAC.2009.2015522
   Web of Science ®Google Scholar
• Curtain, R. F., & Zwart, H. J. (1995). An introduction to infinite-dimensional linear systems theory. Springer-Verlag.
   Google Scholar
• Dabroom, A., & Khalil, H. (2001). Output feedback sampled-data control of nonlinear systems using high-gain observers. IEEE Transactions on Automatic Control, 46(11), 1712–1725. https://doi.org/10.1109/9.964682
   Web of Science ®Google Scholar
• Demetriou, M. (2010). Guidance of mobile actuator-plus-sensor networks for improved control and estimation of distributed parameter systems. IEEE Transactions on Automatic Control, 55(7), 1570–1584. https://doi.org/10.1109/TAC.2010.2042229
   Web of Science ®Google Scholar
• Demetriou, M. (2012). Adaptive control of 2-D PDEs using mobile collocated actuator/sensor pairs with augmented vehicle dynamics. IEEE Transactions on Automatic Control, 57(12), 2979–2993. https://doi.org/10.1109/TAC.2012.2196402
   Web of Science ®Google Scholar
• Demetriou, M., Gatsonis, N., & Court, J. (2014). Coupled controls-computational fluids approach for the estimation of the concentration from a moving gaseous source in a 2-D domain with a Lyapunov-guided sensing aerial vehicle. IEEE Transactions on Control Systems Technology, 22(3), 853–867. https://doi.org/10.1109/TCST.2013.2267623
   Web of Science ®Google Scholar
• Deng, H., Li, H.-X., & Chen, G. (2005). Spectral-approximation-based intelligent modeling for distributed thermal processes. IEEE Transactions on Control Systems Technology, 13(5), 686–700. https://doi.org/10.1109/TCST.2005.847329
   Web of Science ®Google Scholar
• Feng, H., & Guo, B.-Z. (2017). New unknown input observer and output feedback stabilization for uncertain heat equation. Automatica, 86, 1–10. https://doi.org/10.1016/j.automatica.2017.08.004
   Web of Science ®Google Scholar
• Fridman, E. (2010). A refined input delay approach to sampled-data control. Automatica, 46(2), 421–427. https://doi.org/10.1016/j.automatica.2009.11.017
   Web of Science ®Google Scholar
• Fridman, E., & Bar Am, N. (2013). Sampled-data distributed H∞ control of transport reaction systems. SIAM Journal on Control and Optimization, 51(2), 1500–1527. https://doi.org/10.1137/120867639
   Web of Science ®Google Scholar
• Fridman, E., & Blighovsky, A. (2012). Robust sampled-data control of a class of semilinear parabolic systems. Automatica, 48(5), 826–836. https://doi.org/10.1016/j.automatica.2012.02.006
   Web of Science ®Google Scholar
• Gahinet, P., Nemirovskii, A., Laub, A. J., & Chilali, M. (1995). LMI control toolbox for use with Matlab. The Math.Works Inc.
   Google Scholar
• Guo, B.-Z., & Meng, T. (2020). Robust error based non-collocated output tracking control for a heat equation. Automatica, 114, 108818. https://doi.org/10.1016/j.automatica.2020.108818
   Google Scholar
• Hou, L., Michel, A., & Ye, H. (1997). Some qualitative properties of sampled-data control systems. IEEE Transactions on Automatic Control, 42(12), 1721–1725. https://doi.org/10.1109/9.650026
   Web of Science ®Google Scholar
• Hu, L.-S., Lam, J., Cao, Y.-Y., & Shao, H.-H. (2003). A linear matrix inequality (LMI) approach to robust H2 sampled-data control for linear uncertain systems. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, 33(1), 149–155. https://doi.org/10.1109/TSMCB.2003.808181
   PubMed Web of Science ®Google Scholar
• Jin, F.-F., & Guo, B.-Z. (2018). Performance boundary output tracking for one-dimensional heat equation with boundary unmatched disturbance. Automatica, 96, 1–10. https://doi.org/10.1016/j.automatica.2018.06.020
   Web of Science ®Google Scholar
• Kharkovskaia, T., Efimov, D., Fridman, E., Polyakov, A., & Richard, J.-P. (2020). Interval observer design and control of uncertain non-homogeneous heat equations. Automatica, 111, 108595. https://doi.org/10.1016/j.automatica.2019.108595
   Google Scholar
• Krstic, M., & Smyshlyaev, A. (2008). Boundary control of PDEs-A course on backstepping designs. SIAM.
   Google Scholar
• Lam, H. (2012). Stabilization of nonlinear systems using sampled-data output-feedback fuzzy controller based on polynomial-fuzzy-model-based control approach. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, 42(1), 258–267. https://doi.org/10.1109/TSMCB.2011.2163796
   PubMed Web of Science ®Google Scholar
• Li, Z., Teng, J., Qiu, J., & Gao, H. (2020). Filtering design for multirate sampled-data systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 50(11), 4224–4232. https://doi.org/10.1109/TSMC.6221021
   Web of Science ®Google Scholar
• Pisano, A., & Orlov, Y. (2017). On the ISS properties of a class of parabolic DPS' with discontinuous control using sampled-in-space sensing and actuation. Automatica, 81, 447–454. https://doi.org/10.1016/j.automatica.2017.04.025
   Web of Science ®Google Scholar
• Selivanov, A., & Fridman, E. (2016). Distributed event-triggered control of diffusion semilinear PDEs. Automatica, 68, 344–351. https://doi.org/10.1016/j.automatica.2016.02.006
   Web of Science ®Google Scholar
• Selivanov, A., & Fridman, E. (2017). Sampled-data relay control of diffusion PDEs. Automatica, 82, 59–68. https://doi.org/10.1016/j.automatica.2017.04.022
   Web of Science ®Google Scholar
• Selivanov, A., & Fridman, E. (2018). Sampled-data H∞ filtering of a 2D heat equation under pointlike measurements. In 2018 IEEE conference on decision and control (pp. 539–544). IEEE.
   Google Scholar
• Selivanov, A., & Fridman, E. (2019). Delayed H∞ control of 2D diffusion systems under delayed pointlike measurements. Automatica, 109, Article ID 108541. https://doi.org/10.1016/j.automatica.2019.108541
   Google Scholar
• Vazquez, R., & Krstic, M. (2008). Control of turbulent and magnetohydrodynamic channel flows. Birkhäuser.
   Google Scholar
• Voulgaris, P. (1994). Control of asynchronous sampled data systems. IEEE Transactions on Automatic Control, 39(7), 1451–1455. https://doi.org/10.1109/9.299632
   Web of Science ®Google Scholar
• Wang, J.-W., Guo, Y., Fahad, M., & Bingham, B. (2019). Dynamic plume tracking by cooperative robots. IEEE/ASME Transactions on Mechatronics, 24(2), 609–620. https://doi.org/10.1109/TMECH.2019.2892292
   Web of Science ®Google Scholar
• Wang, J.-W., Liu, Y.-Q., & Sun, C.-Y. (2018a). Observer-based dynamic local piecewise control of a linear parabolic PDE using non-collocated local piecewise observation. IET Control Theory & Applications, 12(3), 346–358. https://doi.org/10.1049/iet-cta.2017.0797
   Web of Science ®Google Scholar
• Wang, J.-W., Liu, Y.-Q., & Sun, C.-Y. (2018b). Pointwise exponential stabilization of a linear parabolic PDE system using non-collocated pointwise observation. Automatica, 93, 197–210. https://doi.org/10.1016/j.automatica.2018.03.015
   Web of Science ®Google Scholar
• Wang, J.-W., Tsai, S.-H., Li, H.-X., & Lam, H.-K. (2018). Spatially piecewise fuzzy control design for sampled-data exponential stabilization of semi-linear parabolic PDE systems. IEEE Transactions on Fuzzy Systems, 26(5), 2967–2980. https://doi.org/10.1109/TFUZZ.2018.2809686
   Web of Science ®Google Scholar
• Wang, J.-W., & Wang, J.-M. (2019). Mixed H2/H∞ sampled-data output feedback control design for a semi-linear parabolic PDE in the sense of spatial L∞ norm. Automatica, 103, 282–293. https://doi.org/10.1016/j.automatica.2019.02.018
   Web of Science ®Google Scholar
• Wang, J.-W., & Wang, J.-M. (2021). Dynamic compensator design of linear parabolic MIMO PDEs in N-dimensional spatial domain. IEEE Transactions on Automatic Control, 66(3), 1399–1406. https://doi.org/10.1109/TAC.2020.2994165
   Web of Science ®Google Scholar
• Wang, Z.-P., & Wu, H.-N. (2015). On fuzzy sampled-data control of chaotic systems via a time-dependent Lyapunov functional approach. IEEE Transactions on Cybernetics, 45(4), 819–829. https://doi.org/10.1109/TCYB.2014.2336976
   PubMed Web of Science ®Google Scholar
• Wang, Z.-P., & Wu, H.-N. (2019). Robust guaranteed cost sampled-data fuzzy control for uncertain nonlinear time-delay systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 49(5), 964–975. https://doi.org/10.1109/TSMC.2017.2703837
   Web of Science ®Google Scholar
• Wang, Z.-P., Wu, H.-N., & Li, H.-X. (2020). Estimator-based H∞ sampled-data fuzzy control for nonlinear parabolic PDE systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 50(7), 2491–2500. https://doi.org/10.1109/TSMC.2018.2818761
   Web of Science ®Google Scholar
• Wu, H.-N., & Wang, Z.-P. (2018). Observer-based H∞ sampled-data fuzzy control for a class of nonlinear parabolic PDE systems. IEEE Transactions on Fuzzy Systems, 26(2), 454–473. https://doi.org/10.1109/TFUZZ.2017.2686337
   Web of Science ®Google Scholar