25-Constrained differential dynamic programming applied to multireservoir control problems.

Abstract

Eversince Bellman's (1957) book on Dynamic Programming (DP), new avenues have opened up for the reservoir operation or control problems. The computational effort required to solve a multireservoir control problem by the D.P. is immense when the dimensions of the problem increases, so much so that it is beyond the capa-city of the present day computers. This aspect has been qualified as "the curse of dimensionality" . Many computational efforts have undergone in the literatures in the past two decades. Most of them either are not out of the problem of "curse of dimentionality" or do not assure convergence to a stationary global optimum. The Constrained Differential Dynamic Programming (Constrained DDP) due to Murray and Yakowitz (1979) and Yokavitz(1986) successfully overcomes this "curse" by successive approximations starting from an initial values of policy and state variables. The convergence to a stationary global optimum has been proved when both the loss function and the constraints are convex.