An efficient Monte Carlo method for optimal control problems with uncertainty

Computational Optimization and Applications

Volumn 26, Issue 3, 2003, Pages 219-230

  Cao, Yanzhao ^a   Hussaini, M Y ^b   Zang, T A ^c  

^a FLORIDA A AND M UNIVERSITY   (United States)

^b FLORIDA STATE UNIVERSITY   (United States)

^c NASA LANGLEY RESEARCH CENTER   (United States)

Author keywords

Burger's equation; Monte Carlo method; Optimal control; Sensitivity derivatives; Uncertainty quantification

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTER SIMULATION; OPTIMAL CONTROL SYSTEMS; PARAMETER ESTIMATION; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES; THEOREM PROVING;

BURGERS EQUATION; SENSITIVITY DERIVATIVE MONTE CARLO METHOD; TAYLOR SERIES EXPANSION; VARIANCE REDUCTION METHOD;

MONTE CARLO METHODS;

EID: 0242416196     PISSN: 09266003     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1026079021836     Document Type: Article

References (14)

1. J. Borggaard, D. Pelletier, and E. Turgeon, "Parametric uncertainty analysis for thermal fluid calculations," Journal of Nonlinear Analysis: Series A Theory and Methods, vol. 47, no. 7, pp. 4533-4543, 2001.
2. Y. Cao and M.Y. Hussaini, "On convergence of optimal control problem to exact control problem for systems governed by Navier-Stokes equations," in Proceedings of ICNPPA-2000, 2001, vol. 1, pp. 117-126.
3. Y. Cao and D. Stanescu, "Shape optimization for noise radiation problems," Comp. & Math. Appl., vol. 44, no. 12, pp. 1539-1556, 2002.
4. B. DeVolder, J. Glimm, J. Grove, Y. Kang, Y. Lee, K. Pao, D. Sharp, and K. Ye, "Uncertainty quantification for multiscale simulations," J. Fluids Eng., vol. 124, pp. 29-41, 2002.
5. X. Du and W. Chen, "Towards a better understanding of modeling feasibility robustness in engineering design," Amer. Soc. Mech. Eng., DAC-8565, Sept. 1999.
6. D. Gay, "Algorithm 611, subroutines for unconstrained minimization using a model/trust region approach," ACM Transactions on Mathematical Software, vol. 9, no. 4, pp. 503-524, 1983.
7. J. Glimm and H. Sharp, "Prediction and the quantification of uncertainty," Physica D, vol. 133, pp. 152-170, 1999.
8. M. Gunzburger, "Sensitives, adjoints, and flow optimization," Inter. J. Num. Meth. Fluids., vol. 31, pp. 53-78, 1999.
9. L. Huyse, "Solving problems of optimization under uncertainty as statistical decision problem," AIAA Paper, 2001-1519, 2001.
10. L. Huyse and R. Walters, "Random field solutions including boundary condition uncertainty for the steady state generalized Burgers equation," ICASE Report, 2001-35, 2001.
11. R. Joslin, M. Gunzburger, R. Nicolaides, G. Erlebacher, and M.Y. Hussaini, "A self contained, automated methodology for optimal flow control validated for transition delay," AIAA Journal, vol. 35, pp. 816-824, 1997.
12. A. Parkinson, C. Sorenson, and N. Pourhassan, "A general approach for robust design," J. Mech. Design, vol. 115, no. 1, pp. 74-80, 1993.
13. M. Putko, P. Newman, A. Taylor III, and L. Green, "Approach for uncertainty propagation and robust design in CFD using sensitivity derivatives," AIAA Paper, 2001-2528, 2001.
14. P. Thandedar and S. Kodiyalam, "Structural optimization using probabilistic constraints," Structure Opt., vol. 4, pp. 236-240, 1991.