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This research apply the stochastic optimal control theorem to
obtain a suboptimal policy for the operation of a reservoir
system with uncertainty. The reservoir system will be
formulated as a dynamic linear stochastic system. Although the
traditional discrete type of stochastic dynamic programming
can consider the system uncertainty, it demands large amount
of computational power as the number of state variables
increase, which is the curse of dimensionality. The
deterministic differential dynamic programming can overcome
the computational limitation but it cannot consider the system
uncertainty. Therefore, to ease the computational limitation
and consider the system uncertainty, this study develops a
Constrained Stochastic Differential Dynamic Programming（CSDDP）
algorithm by integrating the Linear Quadratic Gaussian（LQG）
method and Constrained Differential Dynamic Pro- gramming （
CDDP）. The LQG method use the separation theorem to
decompose the problem into an estimator and an actuator. The
estimator is to estimate the expected value of the state
variables and the actuator compute the optimal control by
multiply the estimated expected states with the system gain
matrix. The traditional LQG method can only solve a problem
with quadratic objective function and without unequal sign
constraints. The study combine the LQG method with the CDDP
scheme to develop a CSDDP algorithm. The CSDDP algorithm can
consider the system uncertainty and solve a optimal control
problem with high order objective function and unequal sign
constraints.This research will select the simplified Feitsui-
Shihmen reservoir system on the Tanshui river basin as a test
example to demonstrate the model capacity.
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