Linear Optimal Estimation of Discrete-time Systems with Multiple Measurement Delays
作者单位：School of Control Science and EngineeringShandong University School of Electrical and Electronic EngineeringNanyang Technological University
会议名称：《第36届中国控制会议》
会议届次：36
主办单位：Dalian University of Technology;Systems Engineering Society of China (SESC);Technical Committee on Control Theory (TCCT), Chinese Association of Automation (CAA)
会议日期：2017年
学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学]
关 键 词：Riccati Equation Delay Systems Optimal Estimation
摘 要：In this paper, we consider an optimal estimation problem in the sense of least mean square error for linear discrete-time systems with multiple state delays in the measurement output. Since computation complexity is high for augmentation approach,a lot of researches have been dedicated to finding alternative ways for the optimal estimation design. In existing studies, two dimensional Riccati iteration is unavoidable for calculating the optimal gain. Meanwhile, in the continuous-time setting, the counterpart of the two dimensional Riccati equation is partial differential equation which is difficult to solve. We shall provide a new result that the gain of the optimal estimation is obtained in terms of the solution of a Retarded Riccati-like equation instead of two dimensional Riccati equation. Furthermore, by applying the result to single delay case, we have found a relationship between optimal estimation of systems with multiple delays and optimal prediction.