POD-based feedback control of the burgers equation by solving the evolutionary HJB equation

Computers and Mathematics with Applications

Volumn 49, Issue 7-8, 2005, Pages 1113-1126

  Kunisch, K ^a   Xie, L ^a  

^a UNIVERSITY OF GRAZ   (Austria)

Author keywords

Burgers equation; Closed loop control; Dynamic programming; Hamilton Jacobi Bellman equation; Proper orthogonal decomposition

Indexed keywords

CLOSED LOOP CONTROL SYSTEMS; COMPUTATIONAL COMPLEXITY; DYNAMIC PROGRAMMING; HAMILTONIANS; MATHEMATICAL MODELS; PROBLEM SOLVING;

BURGERS EQUATION; HAMILTON-JACOBI-BELLMAN (HJB) EQUATION; MODEL REDUCTION; PROPER ORTHOGONAL DECOMPOSITION;

FEEDBACK CONTROL;

EID: 23344449930     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2004.07.022     Document Type: Article

References (22)

1. H.V. Ly, and H.T. Tran Proper orthogonal decomposition for flow calculations and optimal control in a horizontal CVD reactor Quart. Appl. Math. 60 4 2002 631 656
2. S.C. Beeler, H.T. Tran, and H.T. Banks Feedback control methodologies for nonlinear systems J. Optim. Theory Appl. 107 1 2000 1 33
3. K. Zhou, J.C. Doyle, and K. Glover Robust and Optimal Control 1996 Prentice Hall The Netherlands
4. K. Ito, and J.D. Schröter Reduced order feedback synthesis for viscous incompressible flows Mathl. Comput. Modelling 33 1-3 2001 173 192
5. J.K. Atwell, and B.B. King Proper orthogonal decomposition for reduced basis feedback controllers for parabolic equations Mathl. Comput. Modelling 33 1-3 2001 1 19
6. H.V. Ly, and H.T. Tran Modelling and control of physical processes using proper orthogonal decomposition Mathl. Comput. Modelling 33 1-3 2001 223 236
7. K. Kunisch, and S. Volkwein Control of Burgers' equation by a reduced-order approach using Proper Orthogonal decomposition J. Optim. Theory and Appl. 102 1998 345 371
8. K. Kunisch, and S. Volkwein Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics SIAM J. Numer. Anal. 40 2002 492 515
9. C.-S. Huang, S. Wang and K.L. Teo, Solving Hamilton-Jacobi-Bellman equations by a modified method of characteristics, (preprint).
10. S. Wang, F. Gao and K.L. Teo, An upwind finite difference method for the approximation of viscosity solutions to Hamilton-Jacobi-Bellman equations, (preprint).
11. M. Bardi, and I. Capuzzo-Dolcetta Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations 1997 Systems & Control: Foundations & Applications, Birkhäuser New Jersey
12. H.-Z. Tang, T. Tang and P. Zhang, An adaptive mesh redistribution method for nonlinear Hamilton-Jacobi equations in two- and three-dimensions, (preprint).
13. S. Gottlieb, and C.-W. Shu Total variation diminishing Runge-Kutta schemes ICASE Report 96-50 1996
14. G.-S. Jiang, and D. Peng Weighted ENO schemes for Hamilton-Jacobi equations SIAM J. Scientific Computing 21 2000 2126 2143
15. G. Berkooz, P. Holmes, and J.L. Lumley Turbulence, Coherent Structures, Dynamical Systems and Symmetry, Cambridge Monographs on Mechanics 1996 Cambridge University Press
16. R. Dautray, and J.-L. Lions Mathematical Analysis and Numerical Methods for Science and Technology, Volume 5: Evolution Problems I 1992 Springer-Verlag
17. R. Temam Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Volume 68 of Applied Mathematical Sciences 1988 Springer-Verlag Berlin
18. A. Kurganov, S. Noelle, and G. Petrova Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations SIAM J. Sci. Comput. 23 3 2001 707 740
19. S. Volkwein Lagrange-SQP techniques for the control constrained optimal control problems for the Burgers equation Computational Optimization and Applications 26 2003 253 284
20. S. Volkwein Second-order conditions for boundary control problem of the Burgers equation Control and Cybernetics 30 2001 249 278
21. T. Furlani, Introduction to Parallel Computing at CCR, http://www.ccr.buffalo.edu/documents/CCR-parallel-process_intro.pdf.
22. E. Heiberg, Matlab Parallization Toolkit, http://hem.passagen.se/ einar_heiberg/.