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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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