Abstract
This paper investigates the linear quadratic (LQ) tracking problem for linear continuous-time systems with pointwise time-varying input delays. It is assumed that the time-varying input delay takes only one value from a finite set at a given time instant. By defining an indicator, the investigated LQ tracking problem is firstly transformed into a special optimal control problem for continuous-time systems with multiple delays in a single input channel. Then the duality between the LQ tracking for the system with multiple input delay and the smoothing for an associated backward delay free system is established. Finally, an explicit analytical solution to the proposed LQ tracking problem is presented by solving the smoothing problem.
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