A spatial domain decomposition approach to distributed H_∞ observer design of a linear unstable parabolic distributed parameter system with spatially discrete sensors

References

• Apostol, T.M. (1974). Mathematical analysis (2nd ed.). Boston, MA: Addison-Wesley.
   Google Scholar
• Chen, B.-S., & Chang, Y.-T. (2009). Fuzzy state-space modeling and robust observer-based control design for nonlinear partial differential systems. IEEE Transactions on Fuzzy Systems, 17(5), 1025–1043.
   Web of Science ®Google Scholar
• Chen, B.-S., Chen, W.-H., & Zhang, W. (2012). Robust filter for nonlinear stochastic partial differential systems in sensor signal processing: Fuzzy approach. IEEE Transactions on Fuzzy Systems, 20(5), 957–970.
   Web of Science ®Google Scholar
• Chen, W.-H., & Chen, B.-S. (2012). Robust filter for linear stochastic partial differential systems via a set of sensor measurements. IEEE Transactions on Circuits and Systems I: Regular Papers, 59(6), 1251–1264.
   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.
   Web of Science ®Google Scholar
• Christofides, P.D. (2001). Nonlinear and robust control of PDE systems: Methods and applications to transport-reaction processes. Boston, MA: Birkhauser.
   Google Scholar
• Demetriou, M.A. (2010a). Design of consensus and adaptive consensus filters for distributed parameter systems. Automatica, 46(2), 300–311.
   Web of Science ®Google Scholar
• Demetriou, M.A. (2010b). 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.
   Web of Science ®Google Scholar
• Demetriou, M.A., Gatsonis, N.A., & Court, J.R. (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.
   Web of Science ®Google Scholar
• Demetriou, M.A., & Hussein, I.I. (2009). Estimation of spatially distributed processes using mobile spatially distributed sensor network. SIAM Journal on Control and Optimization, 48(1), 266–291.
   Web of Science ®Google Scholar
• 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.
   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.
   Web of Science ®Google Scholar
• Gahinet, P., Nemirovskii, A., Laub, A.J., & Chilali, M.,   (1995). LMI control toolbox for use with Matlab. Natick, MA: The Math Works.
   Google Scholar
• Gajic, Z., & Lelic, M. (1996). Modern control system engineering. London: Prentice Hall.
   Google Scholar
• Guo, B.-Z., & Jin, F.-F. (2015). Output feedback stabilization for one-dimensional wave equation subject to boundary disturbance. IEEE Transactions on Automation and Control, 60(3), 824–830.
   Web of Science ®Google Scholar
• Hardy, G., Littlewood, J.E., & Polya, G. (1952). Inequalities (2nd ed). Cambridge: Cambridge University Press.
   Google Scholar
• Hidayat, Z., Babuska, R., De Schutter, B., & Nunez, A. (2011). Observers for linear distributed-parameter systems: A survey. In IEEE international symposium on robotic and sensors environments. (pp. 166–171). Montreal, Canada: IEEE.
   Google Scholar
• Ho, S.-J., & Chen, B.-S. (2016). Robust fuzzy H∞ estimator-based stabilization design for nonlinear parabolic partial differential systems with different boundary conditions. IEEE Transactions on Fuzzy Systems, 24(1), 208–222.
   Web of Science ®Google Scholar
• Hou, M., Zitek, P., & Patton, R. (2002). An observer design for linear time-delay systems. IEEE Transactions on Automatic Control, 47(1), 121–125.
   Web of Science ®Google Scholar
• Kalman, R.E. (1960). A new approach to linear filtering and prediction problems. Transactions of the ASME–Journal of Basic Engineering, 82, 35–45.
   Google Scholar
• Krstic, M., & Smyshlyaev, A. (2008). Boundary control of PDEs-A course on backstepping designs. Philadelphia, PA: SIAM.
   Google Scholar
• Li, H.-X., & Qi, C. (2010). Modeling of distributed parameter systems for applications – a synthesized review from time-space separation. Journal Process Control, 20(8), 891–901.
   Web of Science ®Google Scholar
• Liu, Z., & Zheng, S. (1999). Semigroups associated with dissipative systems. Boca Raton, FL: Chapman and Hall/CRC.
   Google Scholar
• Luenberger, D.G. (1964). Observing the state of a linear system. IEEE Transactions on Military Electronics, 8(2), 74–80.
   Google Scholar
• Meurer, T. (2013). On the extended Luenberger-type observer for semi-linear distributed-parameter systems. IEEE Transactions on Automatic Control, 58(7), 1732–1743.
   Web of Science ®Google Scholar
• Misawa, E.A., & Hedrick, J.K. (1989). Nonlinear observers-A state-of-the art survey. Journal of Dynamic Systems Measurement and Control–Transactions of the ASME, 111(3), 344–352.
   Web of Science ®Google Scholar
• Padhi, R., & Ali, S.F. (2009). An account of chronological developments in control of distributed parameter systems. Annual Reviews in Control, 33(1), 59–68.
   Web of Science ®Google Scholar
• Pazy, A. (1983). Semigroups of linear operators and applications to partial differential equations. New York, NY: Springer-Verlag.
   Google Scholar
• Ray, W.H. (1981). Advanced process control. New York, NY: McGraw-Hill.
   Google Scholar
• Sename, O. (2001). New trends in design if observers for time-delay systems. Kybernetika, 37(4), 427–458.
   Web of Science ®Google Scholar
• Spurgeon, S.K. (2008). Sliding mode observers: A survey. International Journal of Systems Science, 39(8), 751–764.
   Web of Science ®Google Scholar
• Stefani, R., Shahian, B., Savant, J., & Hostetter, G. (2002). Design of feedback control systems. New York, NY: Oxford University Press.
   Google Scholar
• Wang, J.-W., Liu, Y.-Q., & Sun, C.-Y. (2016). Luenberger observer design for state estimation of a linear parabolic distributed parameter system with discrete measurement sensors. In 12th World Congress on intelligent control and automation. (pp. 1123–1128). Guilin, China: IEEE.
   Google Scholar
• Wang, J.-W., & Wu, H.-N. (2014). Lyapunov-based design of locally collocated controllers for semi-linear parabolic PDE systems. Journal of The Franklin Institute, 351(1), 429–441.
   Web of Science ®Google Scholar
• Wang, J.-W., Wu, H.-N., & Li, H.-X. (2013). Guaranteed cost distributed fuzzy observer-based control for a class of nonlinear spatially distributed processes. AIChE Journal, 59(7), 2366–2378.
   Web of Science ®Google Scholar
• Wu, H.-N., & Li, H.-X. (2008). H∞ fuzzy observer-based control for a class of nonlinear distributed parameter systems with control constraints. IEEE Transactions on Fuzzy Systems, 16(2), 502–516.
   Web of Science ®Google Scholar
• Wu, H.-N., & Li, H.-X. (2011). Robust adaptive neural observer design for a class of nonlinear parabolic PDE systems. Journal of Process Control, 21(8), 1172–1182.
   Web of Science ®Google Scholar