ABSTRACT
In this paper, a computational approach is proposed
for solving the discrete-time nonlinear optimal control problem, which is
disturbed by a sequence of random noises. Because of the exact solution of such
optimal control problem is impossible to be obtained, estimating the state
dynamics is currently required. Here, it is assumed that the output can be
measured from the real plant process. In our approach, the state mean
propagation is applied in order to construct a linear model-based optimal
control problem, where the model output is measureable. On this basis, an
output error, which takes into account the differences between the real output
and the model output, is defined. Then, this output error is minimized by
applying the stochastic approximation approach. During the computation
procedure, the stochastic gradient is established, so as the optimal solution
of the model used can be updated iteratively. Once the convergence is achieved,
the iterative solution approximates to the true optimal solution of the
original optimal control problem, in spite of model-reality differences. For
illustration, an example on a continuous stirred-tank reactor problem is
studied, and the result obtained shows the applicability of the approach
proposed. Hence, the efficiency of the approach proposed is highly recommended.