Output feedback control of distributed parameter systems using adaptive proper orthogonal decomposition

Industrial and Engineering Chemistry Research

Volumn 49, Issue 21, 2010, Pages 10496-10509

  Pitchaiah, Sivakumar ^a   Armaou, Antonios ^a  

^a The Pennsylvania State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADAPTIVE PROPER ORTHOGONAL DECOMPOSITION; CONTINUOUS MEASUREMENTS; CONTROL OBJECTIVES; DISTRIBUTED PARAMETER SYSTEMS; EIGEN FUNCTION; FITZHUGH-NAGUMO EQUATIONS; GLOBAL DYNAMICS; OUTPUT FEEDBACK CONTROLS; PROCESS DATA; REDUCED ORDER MODELS; SMALL DATA; STATIC OUTPUT FEEDBACK;

CONTROLLERS; DISTRIBUTED PARAMETER CONTROL SYSTEMS; EIGENVALUES AND EIGENFUNCTIONS; FEEDBACK CONTROL; NONLINEAR CONTROL SYSTEMS; STABILIZATION;

ADAPTIVE CONTROL SYSTEMS;

EID: 78049407663     PISSN: 08885885     EISSN: 15205045     Source Type: Journal    
DOI: 10.1021/ie100463f     Document Type: Conference Paper

References (48)

1. Christofides, P. D. Nonlinear and Robust Control of PDE Systems; Birkhäuser: New York, 2001.
2. Armaou, A. Output Feedback Control Of Dissipative Distributed Processes via Microscopic Simulations Comput. Chem. Eng. 2005, 29, 771-782
3. Armaou, A.; Christofides, P. D. Feedback Control of the Kuramoto-Sivashinsky Equation Physica D 2000, 137, 49-61
4. Christofides, P. D.; Armaou, A. Global Stabilization of the Kuramoto-Sivashinsky Equation Via Distributed Output Feedback Control Syst. Control Lett. 2000, 39, 283-294
5. Armaou, A.; Christofides, P. D. Plasma-Enhanced Chemical Vapor Deposition: Modeling and Control Chem. Eng. Sci. 1999, 54, 3305-3314
6. Temam, R. Infinite-Dimensional Dynamical Systems in Mechanics and Physics; Springer-Verlag: New York, 1988.
7. Balas, M. J. Feedback control of linear diffusion processes Int. J. Control 1979, 29, 523-533
8. Balas, M. J. Nonlinear Finite-Dimensional Control of a class of nonlinear distributed parameter systems using residual mode filters: A proof of local exponential stability J. Math. Anal. Appl. 1991, 162, 63-70
9. Ray, W. H. Advanced Process Control; McGraw-Hill: New York, 1981.
10. Gay, D. H.; Ray, W. H. Identification and control of distributed parameter systems by means of the singular value decomposition Chem. Eng. Sci. 1995, 50, 1519-1539
11. Foias, C.; Jolly, M. S.; Kevrekidis, I. G.; Sell, G. R.; Titi, E. S. On the computation of inertial manifolds Phys. Lett. A 1988, 131, 433-437
12. Titi, E. S. On approximate inertial manifolds to the Navier-Stokes equations J. Math. Anal. Appl. 1990, 149, 540-557
13. Christofides, P. D.; Daoutidis, P. Finite-dimensional control of parabolic PDE systems using approximate inertial manifolds J. Math. Anal. Appl. 1997, 216, 398-420
14. Armaou, A.; Christofides, P. D. Nonlinear Feedback Control of Parabolic PDE Systems with Time-Dependent Spatial Domains J. Math. Anal. Appl. 1999, 239, 124-157
15. Armaou, A.; Christofides, P. D. Finite-Dimensional Control of Nonlinear Parabolic PDE Systems with Time-Dependent Spatial Domains Using Empirical Eigenfunctions Int. J. Appl. Math. Comput. Sci. 2001, 11, 287-317
16. Armaou, A.; Christofides, P. D. Dynamic optimization of dissipative PDE systems using nonlinear order reduction Chem. Eng. Sci. 2002, 57, 5083-5114
17. Sirovich, L. Turbulence and the dynamics of coherent structures: part I, II and III Q. Appl. Math. 1987, XLV, 561-590
18. Holmes, P.; Lumley, J. L.; Berkooz, G. Turbulence, Coherent Structures, Dynamical Systems and Symmetry; Cambridge University Press: New York, 1996.
19. Graham, M. D.; Kevrekidis, I. G. Alternative approaches to the Karhunen-Loève decomposition for model reduction and data analysis Comput. Chem. Eng. 1996, 20, 495-506
20. Rathinam, M.; Petzold, L. R. A new look at proper orthogonal decomposition SIAM J. Numer. Anal. 2003, 41, 1893-1925
21. Balsa-Canto, E.; Alonso, A. A.; Banga, J. R. Reduced-order models for nonlinear distributed process systems and their application in dynamic optimization Ind. Eng. Chem. Res. 2004, 43, 3353-3363
22. Balsa-Canto, E.; Alonso, A. A.; Banga, J. R. Dynamic optimization of complex distributed process systems Chem. Eng. Res. Des. 2005, 83, 724-729
23. Alonso, A. A.; Frouzakis, C. E.; Kevrekidis, I. G. Optimal sensor placement for state reconstruction of distributed process systems AIChE J. 2004, 50, 1438-1452
24. Alonso, A. A.; Kevrekidis, I. G.; Banga, J. R.; Frouzakis, C. E. Optimal sensor location and reduced order observer design for distributed process systems Comput. Chem. Eng. 2004, 28, 27-45
25. Armaou, A.; Christofides, P. D. Wave Suppression by Nonlinear Finite-Dimensional Control Chem. Eng. Sci. 2000, 55, 2627-2640
26. Shvartsman, S. Y.; Kevrekidis, I. G. Nonlinear model reduction for control of distributed systems: a computer-assisted study AIChE J. 1998, 44, 1579-1595
27. Demetriou, M.; Smith, R. Research directions in distributed parameter systems; SIAM Frontiers in Applied Mathematics, 2003.
28. Kirby, M. Minimal dynamical systems from PDEs using Sobolev eigenfunctions Physica D 1992, 57, 466-475
29. Adrover, A.; Giona, M. Modal reduction of PDE models by means of Snapshot Archetypes Physica D 2003, 182, 23-45
30. Varshney, A.; Pitchaiah, S.; Armaou, A. Feedback control of dissipative distributed parameter systems using adaptive model reduction AIChE J. 2008, 55, 906-918
31. Siettos, C. I.; Armaou, A.; Makeev, A. G.; Kevrekidis, I. G. Microscopic/stochastic timesteppers and coarse control: a kinetic Monte Carlo example AIChE J. 2003, 49, 1922-1926
32. Armaou, A.; Siettos, C. I.; Kevrekidis, I. G. Time-steppers and 'coarse' control of distributed microscopic processes Int. J. Robust Nonlin. Control 2004, 14, 89-111
33. Shvartsman, S. Y.; Kevrekidis, I. G. Nonlinear model reduction for control of distributed parameter systems: a computer assisted study AIChE J. 1998, 44, 1579-1595
34. Jolliffe, I. Principal Component Analysis; Springer: New York, 2002.
35. Sontag, E. A "universal" construction of Artstein's theorem on nonlinear stabilization Syst. Control Lett. 1989, 13, 117-123
36. El-Farra, N.; Christofides, P. Robust inverse optimal control of nonlinear systems Int. J. Robust Nonlinear Control 2003, 13, 1371-1388
37. Yuandan, L.; Sontag, E. A universal formula for stabilization with bounded controls Syst. Control Lett. 1991, 16, 393-397
38. Christofides, P.; El-Farra, N. Control of nonlinear and hybrid process systems: Designs for uncertainty, constraints and time delays; Springer: New York, 2005.
39. Chang, H. Nonlinear waves on liquid film-surfaces-.I.Flooding in vertical tube Chem. Eng. Sci. 1986, 41, 2463-2476
40. Sivashinsky, G. Nonlinear analysis of hydrodynamic instability in laminar flames-I. Derivation of basic equations Acta Astronautica 1977, 4, 1117-1206
41. Hooper, A.; Grimshaw, R. Nonlinear instability at the interface between two viscous fluids Phys. Fluids 1985, 28, 37-45
42. Greene, J. M.; Kim, J. S. The steady states of Kuramoto-Sivashinsky equation Physica D 1988, 33, 99-120
43. Chen, L. H.; Chang, H. Nonlinear waves on liquid film surfaces-II. Bifurcation analyses of the long-wave equation Chem. Eng. Sci. 1986, 41, 2477-2486
44. Kevrekidis, I. G.; Nicolaenko, B.; Scovel, J. Back in the saddle again: a computer assited study of the Kuramoto-Sivashinksy equation SIAM J. Appl. Math. 1990, 50, 760-790
45. FitzHugh, R. Impulse and physiological states in models of nerve membrane Biophys. J. 1961, 1, 445-466
46. Nagumo, J.; Arimototo, S.; Yoshizawa, S. An active pulse transmission line simulating nerve axon Proc. Inst. Radio Eng. 1962, 50, 2061-2071
47. Gear, C.; Kevrekidis, I. G.; Theodoropoulou, C. "Coarse" integration/bifurcation analysis via microscopic simulators: micro-Galerkin methods Comput. Chem. Eng. 2002, 26, 941-963
48. Keener, J.; Sneyd, J. Mathematical Physiology; Springer-Verlag: New York, 1998.