Duality between State Estimation and Linear Quadratic Tracking for Time-delay Systems
نویسندگان
چکیده
Abstract This paper investigates the duality between the estimation and linear quadratic tracking problem for time-delay systems. Based on the innovation analysis approach, the linear minimum mean square error estimators including filter and smoother are developed in terms of a forward partial difference Riccati equation. Then the linear quadratic tracking problem for time-delay systems is discussed based on the dynamic programming technique. By employ the estimation approach proposed in this paper, the control gains is given in terms of a backward partial difference Riccati equation. Finally, after comparing the estimation and tracking results, we establish a duality between the estimation problem and the linear quadratic tracking problem for systems with time delay. Our results make it possible to apply estimation algorithms to tracking control problems and vice versa.
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