A numerical approach to an optimal boundary control of the viscous Burgers' equation

Applied Mathematics and Computation

Volumn 210, Issue 1, 2009, Pages 126-135

  Kucuk, Ismail ^a   Sadek, Ibrahim ^a  

^a AMERICAN UNIVERSITY OF SHARJAH   (United Arab Emirates)

Author keywords

Boundary control; Burgers' equation; Control parametrization; Modal expansion technique; Nonlinear partial differential equation; Optimal control

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL FLUID DYNAMICS; DISTRIBUTED PARAMETER CONTROL SYSTEMS; DYNAMICAL SYSTEMS; ELECTRIC CURRENT CONTROL; EQUATIONS OF STATE; FOURIER ANALYSIS; FOURIER SERIES; HARMONIC ANALYSIS; MATHEMATICAL PROGRAMMING; NONLINEAR EQUATIONS; RUNGE KUTTA METHODS; TIME SERIES;

BOUNDARY CONTROL; BURGERS' EQUATION; CONTROL PARAMETRIZATION; MODAL EXPANSION TECHNIQUE; NONLINEAR PARTIAL DIFFERENTIAL EQUATION; OPTIMAL CONTROL;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 61649118951     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2008.12.056     Document Type: Article

References (24)

1. King B.B., and Kruger D.A. Burgers' equation: Galerkin least-squares approximation and feedback control. Mathematical and Computer Modeling 38 (2003) 1075-1085
2. Smaoui N. Nonlinear boundary control of the generalized Burgers equation. Nonlinear Dynamics 37 (2004) 75-86
3. Tian L., Shena C., and Dinga D. Optimal control of the viscouse Camassa-Holm equation. Nonlinear Analysis: Real World Applications 10 1 (2009) 519-530
4. Effati S., Janfada M., Esmaeili M., and Roohparvar H. Solving of optimal control problem of parabolic pdes in exploitation of oil by iterative dynamic programming. Applied Mathematics and Computation 181 1 (2006) 1505-1512
5. Balas M.J. Active control of flexible systems. J. Optim. Theory 25 9 (1978) 415-436
6. Sadek I.S., and Feng J. Modelling techniques for optimal control of distributed parameter systems. Mathematical and Computer Modelling 18 7 (1993) 41-58
7. Dean E.J., and Gubernatis P. Pointwise control of Burger's equation - a numerical approach. Computers and Mathematics with Applications 22 7 (1991) 93-100
8. Park H.M., and Jang Y.D. Control of Burgers equation by means of mode reduction. International Journal of Engineering Science 38 7 (2000) 785-805
9. Kucuk I., and Sadek I. An efficient computational method for the optimal control problem for the Burgers' equation. Mathematical and Computer Modeling 44 11-12 (2006) 973-982
10. Smaoui N. Boundary and distributed control of the viscous Burgers equation. Journal of Computational and Applied Mathematics 182 (2005) 91-104
11. Liu W., and Krstic M. Backstepping boundary control of Burgers' equation with actuator dynamics. Systems and Control Letters 41 (2000) 291-303
12. Balogh A., Gilliam D.S., and Shubov V.I. Stationary solutions for a boundary controlled Burgers' equation. Mathematical and Computer Modeling 33 (2001) 21-37
13. Krstic M. On global stabilization of Burgers' equation by boundary control. Systems and Control Letters 37 3 (1999) 123-141
14. Noack A., and Walther A. Adjoint concepts for the optimal control of Burgers' equation. Comput. Optim. Appl. 36 1 (2007) 109-133
15. J. Atwell, B. King, Stabilized finite methods and feedback control for Burgers' equations, in: Proceedings of the American Control Conference, vol. 4, 2000, pp. 2745-2749.
16. Park H.M., Lee M.W., and Jang Y.D. An efficient computational method of boundary optimal control problems for the Burgers equation. Computer Methods in Applied Mechanics and Engineering 166 (1998) 289-308
17. Fletcher R., and Reeves. Function minimization by conjugate gradients. Computer Journal 7 (1964) 144-160
18. Naylor A.W., and Sell G.R. Linear Operator Theory in Engineering and Sciences, of Applied mathematical sciences vol. 40 (1982), Springer-Verlag, New York
19. Chang Y., and Lee T. Application of general orthogonal polynomials to the optimal control of time-varying linear systems. International Journal of Control 43 4 (1986) 1283-1304
20. Endow Y. Optimal control via Fourier series of operational matrix of integration. IEEE Transactions Automatic Control 34 7 (1989) 770-773
21. Sirisena H.R., and Chou F.S. State parameterization approach to the solution of optimal control problems. Optimal Control Applications and Methods 2 (1981) 289-298
22. Curtain R.F., and Pritchard A.J. Functional Analysis in Modern Applied Mathematics (1977), Academic Press, New York
23. Dormand J.R., and Prince P.J. A family of embedded Runge-Kutta formulae. Journal of Computer Applied Mathematics 6 (1980) 19-26
24. Lagarias J.C., Reeds J.A., Wright M.H., and Wright P.E. Convergence properties of the Nelder-Mead simplex algorithm in low dimensions. SIAM Journal on Optimization 9 (1998) 112-147