Linear quadratic Gaussian control for linear time-delay systems

This study investigates a separation principle for the H₂ control of time-delay systems with partial observations. The authors first consider the linear quadratic regulation problem for time-delay systems. Based on the dynamic programming technique, the solution to the controller is given in terms of a backward partial difference Riccati equation. Then the estimation problem is investigated for linear discrete-time systems in the presence of time-delays. By employing the innovation analysis approach, the linear minimum-mean-square error (LMMSE) estimator is developed in terms of a forward partial difference Riccati equation. The Riccati equation is of the same dimension as the plant. Therefore compared with the conventional augmented approach, the presented approach greatly lessens the computational demand when the delay is large. Finally, they show that the separation principle holds in the following sense: an optimal controller can be obtained from two parts, one associated with the optimal control problem when state variable is available, and the other one associated with the LMMSE estimation problem.