Diagnostic Checking in Stochastic Dynamic Programming
Publication: Journal of Water Resources Planning and Management
Volume 119, Issue 4
Abstract
A testing procedure to diagnose whether the stochastic dynamic programming (SDP) models for reservoir operations will converge is presented. Theoretically, the stability of SDP can be diagnosed by checking whether a coefficient matrix, connected with the existence and uniqueness of solutions of transition probabilities for the inflows, is linearly independent. The steady‐state SDP model of reservoir operations is guaranteed after the SDP convergence has been approved. If the rank of the coefficient matrix is the same as the number of inflow states, there is precisely one solution for the steady‐state distribution of inflows and SDP convergence will be reached. Otherwise, the SDP model is divergent.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Alarcon, L. F. and Marks, D. H. (1979). “A stochastic dynamic programming model for the operation of the High Aswan Dam.” Report No. 246, Dept. of Civil Engrg., MIT, Cambridge, Mass.
2.
Bellman, R., and Dreyfus, S. E. (1962). Applied dynamic programming. Princeton University Press, Princeton, N.J.
3.
Goulter, I. C., and Tai, F. K. (1985). “Practical implications in the use of stochastic dynamic programming for reservoir operations.” Water Resour. Bull., 21(1), 65–74.
4.
He, Q., and Bogardi, J. J. (1988). “The effect of the structure of the transition probability matrices on the convergence of stochastic dynamic programming.” Seminar on: conflict analysis in reservoir management, J. J. Bogardi, ed., Asian Institute of Technology, Bangkok, Thailand.
5.
Huang, W. C. (1989). “Multiobjective decision making in the on‐line operation of a multipurpose reservoir.” PhD thesis, Asian Institute of Technology, Bangkok, Thailand.
6.
Huang, W. C., Harboe, R., and Bogardi, J. J. (1991). “Testing stochastic dynamic programming models conditioned on observed or forecasted inflows.” J. Water Resour. Plng. and Mgmt., ASCE, 117(1), 28–36.
7.
Loucks, D. P., Stedinger, J. R., and Haith, D. A. (1981). Water resources system planning and analysis. Prentice‐Hall Inc., Englewood Cliffs, N.J.
8.
Su, S. Y., and Deininger, R. A. (1974). “Modeling of the regulations of Lake Superior under uncertainty of future water supplies.” Water Resour. Res., 10(1), 11–25.
9.
Wang, D., and Adams, B. J. (1986). “Optimization of real‐time reservoir operations with Markov decision processes.” Water Resour. Res., 22(3), 345–352.
Information & Authors
Information
Published In
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: Feb 4, 1992
Published online: Jul 1, 1993
Published in print: Jul 1993
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.