Abstract
In this paper we investigate the finite horizon linear quadratic regulation (LQR) problem for a linear continuous time system with time-varying delay in control input and a quadratic criterion. We assume that the time-varying delay is of a known upper bound, then the LQR problem is transformed into the optimal control problem for systems with multiple input channels, each of which has single constant delay. The purpose of this paper is to obtain an explicit solution to the addressed LQR problem via establishing a duality principle, which is applied to the optimal smoothing for an associated continuous time system with a multiple delayed measurement.
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