Linear quadratic regulation for linear time-varying systems with multiple input delays part II: continuous-time case

The second part of the paper revisits the LQR problem for continuous-time systems with multiple input delays. Conventionally, the problem was addressed via dynamic programming arguments where no explicit formula for the optimal controller was given. In this paper we provide an explicit formula for the optimal control law by applying an innovation method. It is shown that the complicated LQR problem for systems with multiple input delays is dual to the well known fixed-lag smoothing in Krein space and thus the LQR problem is solved by the standard projection. Our solution to the optimal control involves solving only one standard Riccati differential equation.