- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 418258, 7 pages
Synchronization of the Coupled Distributed Parameter System with Time Delay via Proportional-Spatial Derivative Control
1School of Automation and Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, Southeast University, Nanjing 210096, China
2Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Received 16 December 2013; Revised 27 January 2014; Accepted 9 February 2014; Published 16 March 2014
Academic Editor: Wei Lin
Copyright © 2014 Kun Yuan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J. C. Robinson, “Finite-dimensional behavior in dissipative partial differential equations,” Chaos, vol. 5, no. 1, pp. 330–345, 1995.
- P. D. Christofides, Nonlinear and Robust Control of PDE Systems: Methods and Applications to Transport-Reaction Processes, Birkhäuser, Boston, Mass, USA, 2001.
- H. Deng, H.-X. Li, and G. Chen, “Spectral-approximation-based intelligent modeling for distributed thermal processes,” IEEE Transactions on Control Systems Technology, vol. 13, no. 5, pp. 686–700, 2005.
- C. Antoniades and P. D. Christofides, “Non-linear feedback control of parabolic partial differential difference equation systems,” International Journal of Control, vol. 73, no. 17, pp. 1572–1591, 2000.
- H.-X. Li, H. Deng, and J. Zhong, “Model-based integration of control and supervision for one kind of curing process,” IEEE Transactions on Electronics Packaging Manufacturing, vol. 27, no. 3, pp. 177–186, 2004.
- M. J. Balas, “The Galerkin method and feedback control of linear distributed parameter systems,” Journal of Mathematical Analysis and Applications, vol. 91, no. 2, pp. 527–546, 1983.
- R. F. Curtain, “Finite-dimensional compensator design for parabolic distributed systems with point sensors and boundary input,” IEEE Transactions on Automatic Control, vol. 27, no. 1, pp. 98–104, 1982.
- M. A. Erickson, R. S. Smith, and A. J. Laub, “Finite-dimensional approximation and error bounds for spectral systems with partially known eigenstructure,” IEEE Transactions on Automatic Control, vol. 39, no. 9, pp. 1904–1909, 1994.
- P. D. Christofides and P. Daoutidis, “Finite-dimensional control of parabolic PDE systems using approximate inertial manifolds,” Journal of Mathematical Analysis and Applications, vol. 216, no. 2, pp. 398–420, 1997.
- P. D. Christofides, “Robust control of parabolic PDE systems,” Chemical Engineering Science, vol. 53, no. 16, pp. 2949–2965, 1998.
- P. D. Christofides and J. Baker, “Robust output feedback control of quasi-linear parabolic PDE systems,” Systems & Control Letters, vol. 36, no. 5, pp. 307–316, 1999.
- J. Baker and P. D. Christofides, “Finite-dimensional approximation and control of non-linear parabolic PDE systems,” International Journal of Control, vol. 73, no. 5, pp. 439–456, 2000.
- K. A. Hoo and D. Zheng, “Low-order control-relevant models for a class of distributed parameter systems,” Chemical Engineering Science, vol. 56, no. 23, pp. 6683–6710, 2001.
- H. M. Park and D. H. Cho, “The use of the Karhunen-Loève decomposition for the modeling of distributed parameter systems,” Chemical Engineering Science, vol. 51, no. 1, pp. 81–98, 1996.
- B.-S. Chen and Y.-T. Chang, “Fuzzy state-space modeling and robust observer-based control design for nonlinear partial differential systems,” IEEE Transactions on Fuzzy Systems, vol. 17, no. 5, pp. 1025–1043, 2009.
- K. Yuan, S.-M. Fei, and J.-D. Cao, “Partial synchronization of the distributed parameter system with time delay via fuzzy control,” IMA Journal of Mathematical Control and Information, 2013.
- J.-W. Wang, H.-N. Wu, and H.-X. Li, “Distributed proportional-spatial derivative control of nonlinear parabolic systems via fuzzy PDE modeling approach,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 42, no. 3, pp. 927–938, 2012.
- Y.-T. Chang and B.-S. Chen, “A fuzzy approach for robust reference-tracking-control design of nonlinear distributed parameter time-delayed systems and its application,” IEEE Transactions on Fuzzy Systems, vol. 18, no. 6, pp. 1041–1057, 2010.
- J.-W. Wang, H.-N. Wu, and H.-X. Li, “Distributed fuzzy control design of nonlinear hyperbolic pde systems with application to nonisothermal plug-flow reactor,” IEEE Transactions on Fuzzy Systems, vol. 19, no. 3, pp. 514–526, 2011.
- K. Yuan, H.-X. Li, and J. Cao, “Robust stabilization of the distributed parameter system with time delay via fuzzy control,” IEEE Transactions on Fuzzy Systems, vol. 16, no. 3, pp. 567–584, 2008.
- C. W. Wu and L. O. Chua, “Synchronization in an array of linearly coupled dynamical systems,” IEEE Transactions on Circuits and Systems I, vol. 42, no. 8, pp. 430–447, 1995.
- C. W. Wu, “Synchronization in coupled arrays of chaotic oscillators with nonreciprocal coupling,” IEEE Transactions on Circuits and Systems I, vol. 50, no. 2, pp. 294–297, 2003.
- C. Li and G. Chen, “Synchronization in general complex dynamical networks with coupling delays,” Physica A, vol. 343, no. 1–4, pp. 263–278, 2004.
- E. M. Izhikevich and F. C. Hoppensteadt, “Slowly coupled oscillators: phase dynamics and synchronization,” SIAM Journal on Applied Mathematics, vol. 63, no. 6, pp. 1935–1953, 2003.
- J. Lü and G. Chen, “A time-varying complex dynamical network model and its controlled synchronization criteria,” IEEE Transactions on Automatic Control, vol. 50, no. 6, pp. 841–846, 2005.
- W. Lu and T. Chen, “New approach to synchronization analysis of linearly coupled ordinary differential systems,” Physica D. Nonlinear Phenomena, vol. 213, no. 2, pp. 214–230, 2006.
- K. Wu and B.-S. Chen, “Synchronization of partial differential systems via diffusion coupling,” IEEE Transactions on Circuits and Systems I, vol. 59, no. 11, pp. 2655–2668, 2012.