  Efficiently computing the optimal control policy concerning a complicated
future with stochastic disturbance has always been a challenge. The predicted
stochastic future disturbance can be represented by a scenario tree, but
solving the optimal control problem with a scenario tree is usually
computationally demanding. In this paper, we propose a data-based clustering
approximation method for the scenario tree representation. Differently from the
popular Markov chain approximation, the proposed method can retain information
from previous steps while keeping the state space size small. Then the
predictive optimal control problem can be approximately solved with reduced
computational load using dynamic programming. The proposed method is evaluated
in numerical examples and compared with the method which considers the
disturbance as a non-stationary Markov chain. The results show that the
proposed method can achieve better control performance than the Markov chain
method.
