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Articles

A unified Lyapunov-based design for a dynamic compensator of linear parabolic MIMO PDEs

Pages 1804-1811 | Received 15 May 2019, Accepted 30 Sep 2019, Published online: 10 Oct 2019

References

  • Balakrishnan, V. (2003). All about the Dirac delta function (?). Resonance, 8(8), 48–58. doi: 10.1007/BF02866759
  • Balas, M. (1978). Feedback control of flexible systems. IEEE Transactions on Automatic Control, 23(4), 673–679. doi: 10.1109/TAC.1978.1101798
  • Banks, H. (1975). Modeling and control in the biomedical sciences. New York: Springer-Verlag.
  • Christofides, P. (2001). Nonlinear and robust control of PDE systems: Methods and applications to transport-reaction processes. Boston, MA: Birkhäuser.
  • Demetriou, M. A. (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. doi: 10.1109/TAC.2010.2042229
  • Demetriou, M. A. (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. doi: 10.1109/TAC.2012.2196402
  • Fridman, E., & Am, N. B. (2013). Sampled-data distributed H∞ control of transport reaction systems. SIAM Journal on Control and Optimization, 51(2), 1500–1527. doi: 10.1137/120867639
  • Fridman, E., & Blighovsky, A. (2012). Robust sampled-data control of a class of semilinear parabolic systems. Automatica, 48(5), 826–836. doi: 10.1016/j.automatica.2012.02.006
  • Gahinet, P., Nemirovskii, A., Laub, A. J., & Chilali, M. (1995). LMI control toolbox for use with Matlab. Natick MA: The Math.Works Inc.
  • He, W., Ge, S. S., How, B. V. E., & Choo, Y. S. (2014). Dynamics and control of mechanical systems in offshore engineering. London: Springer-Verlag.
  • Krstic, M., Guo, B.-Z., Balogh, A., & Smyshlyaev, A. (2008). Control of a tip-force destabilized shear beam by observer-based boundary feedback. SIAM Journal on Control and Optimization, 47(2), 553–574. doi: 10.1137/060676969
  • Krstic, M., & Smyshlyaev, A. (2008). Boundary control of PDEs-A course on backstepping designs. Philadelphia: SIAM.
  • Lasiecka, I (1995, December). Control of systems governed by partial differential equations: A historical perspective. Proceedings of the 34th IEEE conference on decision and control (Vol. 3, pp. 2792–2796). New Orleans, LA: IEEE.
  • Li, H.-X., & Qi, C. (2010). Modeling of distributed parameter systems for applications – A synthesized review from time-space separation. Journal of Process Control, 20(8), 891–901. doi: 10.1016/j.jprocont.2010.06.016
  • Liu, Y.-Q., Wang, J.-W., & Sun, C.-Y. (2018). Observer-based output feedback compensator design for linear parabolic PDEs with local piecewise control and pointwise observation in space. IET Control Theory & Applications, 12(13), 1812–1821. doi: 10.1049/iet-cta.2017.1358
  • Liu, Y.-Q., Wang, J.-W., & Sun, C.-Y. (2019). A Lyapunov-based design of dynamic feedback compensator for linear parabolic MIMO PDEs. IMA Journal of Mathematical Control and Information. Advance online publication. doi:10.1093/imamci/dnz008
  • Padhi, R., & Ali, Sk. F. (2009). An account of chronological developments in control of distributed parameter systems. Annual Reviews in Control, 33(1), 59–68. doi: 10.1016/j.arcontrol.2009.01.003
  • Pazy, A. (1983). Semigroups of linear operators and applications to partial differential equations. New York: Springer-Verlag.
  • 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. doi: 10.1016/j.automatica.2017.04.025
  • Ray, W. H. (1981). Advanced process control. New York: McGraw-Hill.
  • Tucsnak, M., & Weiss, G. (2009). Observation and control for operator semigroups. Basel: Birkäuser Verlag AG.
  • Verica, R.-G., Karagiannis, D. A., Cheng, M.-B., & Su, W.-C (2014). Recent trends in stabilization and control of distributed parameter dynamic systems. ASME 2014 international mechanical engineering congress and exposition (V04AT04A004(8)). Montreal, QC: American Society of Mechanical Engineers.
  • Wang, J.-W., & Li, H.-X. (2019). Static collocated piecewise fuzzy control design of quasi-linear parabolic PDE systems subject to periodic boundary conditions. IEEE Transactions on Fuzzy Systems, 27(7), 1479–1492. doi: 10.1109/TFUZZ.2018.2881667
  • 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. doi: 10.1049/iet-cta.2017.0797
  • 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. doi: 10.1016/j.automatica.2018.03.015
  • 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. doi: 10.1109/TFUZZ.2013.2269698
  • Xu, G.-Q., & Yung, S. (2003). Stabilization of Timoshenko beam by means of pointwise controls. ESIAM: Control, Optimisation and Calculus of Variations, 9, 579–600.

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