Advances in Pure Mathematics, 2019, 9, 317-329 http://www.scirp.org/journal/apm ISSN Online: 2160-0384 ISSN Print: 2160-0368 DOI: 10.4236/apm.2019.94014 Apr. 11, 2019 317 Advances in Pure Mathematics An Expanded Optimal Control Policy for a Coupled Tanks System with Random Disturbance Sie Long Kek 1 , Sy Yi Sim 2 , Chuei Yee Chen 3 1 Department of Mathematics and Statistics, Universiti Tun Hussein Onn Malaysia, Pagoh, Malaysia 2 Department of Electrical Engineering Technology, Universiti Tun Hussein Onn Malaysia, Pagoh, Malaysia 3 Department of Mathematics, Universiti Putra Malaysia, Serdang, Malaysia Abstract In this paper, an expanded optimal control policy is proposed to study the coupled tanks system, where the random disturbance is added into the sys- tem. Since the dynamics of the coupled tanks system can be formulated as a nonlinear system, determination of the optimal water level in the tanks is useful for the operation decision. On this point of view, the coupled tanks system dynamics is usually linearized to give the steady state operating height. In our approach, a model-based optimal control problem, which is adding with adjusted parameters, is considered to obtain the true operating height of the real coupled tanks system. During the computation procedure, the differences between the real plant and the model used are measured re- peatedly, where the optimal solution of the model used is updated. On this basis, system optimization and parameter estimation are integrated. At the end of the iteration, the iterative solution approximates to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. In conclusion, the efficiency of the approach proposed is shown. Keywords Expanded Optimal Control, Coupled Tanks System, Model-Reality Differences, Iterative Solution, Adjusted Parameters 1. Introduction A coupled tanks system, which consists of a joint of two tanks together through pipes in order to reserve water at the operating height level, is an important study in the control engineering and process industries [1]. The applications of How to cite this paper: Kek, S.L., Sim, S.Y. and Chen, C.Y. (2019) An Expanded Op- timal Control Policy for a Coupled Tanks System with Random Disturbance. Ad- vances in Pure Mathematics, 9, 317-329. https://doi.org/10.4236/apm.2019.94014 Received: March 4, 2019 Accepted: April 8, 2019 Published: April 11, 2019 Copyright © 2019 by author(s) and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access