## Study on Discrete-Time Nonlinear Stochastic Optimal Control Problem Based on Stochastic Approximation Approach

An fascinating research subject is the nonlinear optimal control problem, which is interrupted by random noises. In the presence of random sounds, it was not possible to calculate precisely the entire state trajectory. A theoretical approach for solving the discrete-time nonlinear optimal control problem is proposed in this paper, which is interrupted by a series of random noises. Since it is impossible to obtain the exact solution to such an optimal control problem, estimating the dynamics of the state is currently necessary. Here, it is believed that the output from the actual plant process can be calculated. In our strategy, in order to construct a linear model-based optimal control problem, where the model output is measurable, the state mean propagation is used. An output error that takes account of the differences between the actual output and the model output is defined on this basis. Then, applying the stochastic approximation approach, this output error is minimised. The stochastic gradient is defined during the computation process, in order to iteratively update the optimal solution of the model used. Once the convergence is reached, in spite of model-reality variations, the iterative solution approximates the true optimal solution of the original optimal control problem. An example of a continuous stirred-tank reactor problem is examined for illustration, and the result obtained shows the applicability of the proposed solution. The efficiency of the proposed solution is, therefore, strongly recommended.

**Author(s) Details**

**Sie Long Kek
**Department of Mathematics and Statistics, Universiti Tun Hussein Onn Malaysia, Pagoh, Malaysia.

**Sy Yi Sim
**Department of Electrical Engineering Technology, Universiti Tun Hussein Onn Malaysia, Pagoh, Malaysia.

**Wah June Leong**

Department of Mathematics, Universiti Putra Malaysia, Serdang, Malaysia.

**Professor Kok Lay Teo
**Department of Mathematics and Statistics, Curtin University of Technology, Perth, Australia.

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iterative solution model-reality differences Nonlinear optimal control output error stochastic approximation.