This paper considers the application of the preview control method to the optimal tracking control problem for a class of continuous-time systems with state and input delays. First, through a transformation, the system is transformed into a nondelayed one. Then, the tracking problem of the time-delay system is transformed into one of a nondelayed system via processing of the reference signal. We then apply preview control theory to derive an augmented system for the nondelayed system and design a controller with preview function assuming that the reference signal is previewable. Finally, we obtain the optimal control law of the augmented error system and thus obtain that of the original system by letting the preview length of the reference signal go to zero. Numerical simulations are provided to illustrate the effectiveness and validity of our conclusions.
In this paper, the optimal tracking control problem for discrete-time with state and input delays is studied based on the preview control method. First, a transformation is introduced. Thus, the system is transformed into a non-delayed system and the tracking problem of the time-delay system is transformed into the regulation problem of a non-delayed system via processing of the reference signal. Then, by applying the preview control theory, an augmented system for the non-delayed system is derived, and a controller with preview function is designed, assuming that the reference signal is previewable. Finally, the optimal control law of the augmented error system and the optimal control law of the original system are obtained by letting the preview length of the reference signal go to zero.
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