离散时滞系统线性估计与线性二次调节问题的对偶原理

his paper investigates the duality between the estimation and control problems for time-delay systems.We first consider the estimation problem for linear discrete-time systems in the presenceof multiplicative noise and time delays, where the delays appear in both state and measurementequations. Based on the innovation analysis approach, the linear minimum mean square error estimators are developed in terms of a forward partial difference Riccati equationand a forward Lyapunov equation.Then the linear quadratic regulation (LQR) problem for deterministic time-delay systems is discussed based on the dynamic programming technique, and the controlleris given in terms of a backward partial difference Riccati equation and a backward Lyapunov equation. Finally,after comparing the estimation and control results, we establish a dualitybetween the estimation problem for time-delay systems with multiplicative noise andthe LQR problem for deterministic time-delay systems with constraint conditions.