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Discrete Differential Dynamic Programing Approach to Water Resources Systems Optimization
Author(s) -
Heidari Manoutchehr,
Chow Ven Te,
Kokotović Petar V.,
Meredith Dale D.
Publication year - 1971
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr007i002p00273
Subject(s) - trajectory , computer science , mathematical optimization , set (abstract data type) , trajectory optimization , invertible matrix , dynamic programming , kleene's recursion theorem , algorithm , mathematics , optimal control , physics , astronomy , pure mathematics , programming language
The optimization of operating policies of multiple unit and multiple purpose water resources systems by traditional dynamic programing with the use of high speed digital computers encounters two major difficulties: memory requirements and computer time requirements. This paper presents an iterative method that can ease the above difficulties considerably. The method starts with a trial trajectory satisfying a specific set of initial and final conditions and applies Bellman's recursive equation in the neighborhood of this trajectory. At the end of each iteration step a locally improved trajectory is obtained and used as the trial trajectory in the next step. The method has proved particularly effective in the case of so‐called ‘invertible’ systems. The merits of the proposed approach are demonstrated through its application to a four‐unit, two‐purpose water resources system. To save computer time the example is restricted to deterministic inflows.