573 Optimal Control of Discrete-Time Linear Stochastic Dynamic System with Model-Reality Differences Sie-Long Kek 1 + , Mohd Ismail Abdul Aziz 2 1 Department of Mathematics, Centre for Science Studies, Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja, Batu Pahat, Johor Darul Takzim, Malaysia. 2 Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor Darul Takzim, Malaysia. Abstract. A rapid development of digital computer has brought great changes to the control systems. The control schemes are altered from optimizing the continuous-time dynamic system to discretization design of continuous plants. Also, there are many processes in discrete nature and only can be solved by discrete time controller. In this paper, a discussion of optimal control of discrete-time linear stochastic dynamic system is made. We modify the novel optimal control algorithm which developed by Roberts [1] and Becerra [2] to obtain the solution of linear stochastic dynamic system in spite of model-reality differences. This extension principle of model-reality differences is taking into account the state estimation by Kalman filtering, and integrating the system optimization and parameter estimation to give the optimum of real plant. During the iterative computations, the model-based optimal control problem is solving in which the real optimum is obtained after the convergence is achieved. A scalar example is presented and the resulting graphical solutions show that the proposed algorithm is efficient to provide the optimum of real plant. Keywords: stochastic linear optimal control, principle of model-reality differences 1. Introduction Optimization and control of stochastic system are challenge work. Since finding the optimal decision to minimize the cost functional subject to a set of dynamic state that disturbed by random noises is more difficult rather than deterministic situation. We can measure the entire state and suggest the admissible of decision ideally under linear quadratic regulator (LQR) approximation optimization. However, in presence of random disturbances, our decision is not necessary appropriate. The principle of model-reality differences approach, known as DISOPE (dynamic integrated system optimization and parameter estimation), leads the nonlinear optimal control problems to be solved without random disturbances. It takes into account the different structural and parameters between the real plant and the model used in its iterative computations. The repeated solution generated by system optimization and parameter estimation converges to the correct real optimum in spite of the differences among the model used and real plant. In this manner, we only solve the modified model-based optimal control problem in order to obtain the optimum of real plant [1], [2]. Integrate the system optimization and parameter estimation with consideration of the random environment inspires us to investigate the optimization and control stochastic system. In this paper, we analyze a modification of the principle of model-reality differences and propose the extension principle to overcome the problems of stochastic control in spite of differences between the estimated real plant and the model used. + Corresponding author. E-mail address: slkek@uthm.edu.my 2009 International Conference on Machine Learning and Computing IPCSIT vol.3 (2011) © (2011) IACSIT Press, Singapore