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This paper discusses the optimal preview control problem for a class of linear continuous stochastic control systems in the infinite horizon, based on the augmented error system method. Firstly, an assistant system is designed and the state equation is translated to the assistant system. Then, an integrator is introduced to construct a stochastic augmented error system. As a result, the tracking problem is converted to a regulation problem. Secondly, the optimal regulator is solved based on dynamic programming principle for the stochastic system, and the optimal preview controller of the original system is obtained. Compared with the finite horizon, we simplify the performance index. We also study the stability of the stochastic augmented error system and design the observer for the original stochastic system. Finally, the simulation example shows the effectiveness of the conclusion in this paper.

Optimal Preview Control for a Class of Linear Continuous Stochastic Control Systems in the Infinite Horizon