In this paper, we provide a separation theorem for the singular linear quadratic （LQ） control problem of ItS-type linear systems in the case of the state being partially observable. Above all, the Kalmam Bucy filter...In this paper, we provide a separation theorem for the singular linear quadratic （LQ） control problem of ItS-type linear systems in the case of the state being partially observable. Above all, the Kalmam Bucy filtering of the dynamics is given by means of Girsanov transformation, by which the suboptimal feedback control of the LQ problem is determined. Furthermore, it is shown that the well-posedness of the LQ problem is equivalent to the solvability of a generalized differential Riccati equation （GDRE）.展开更多
基金supported by the Natural Science Foundation of Shandong Province(Grant Nos.ZR2020MA032,ZR2022MA029)the National Natural Science Foundation of China(Grant No.72171133)the high-quality course for postgraduate education in Shandong Province《Intermediate Econometrics(Graded Teaching)》(SDYKC21137).
基金Supported by the National Natural Science Foundation of China (Grant No. 61174078)the Mathematical Tianyuan Youth Foundation of China (Grant No. 11126094)+1 种基金the Key Project of Natural Science Foundation of Shandong Province (Grant No. ZR2009GZ001)the research project of "SDUST Spring Bud" (Grant No.2009AZZ074)
文摘In this paper, we provide a separation theorem for the singular linear quadratic （LQ） control problem of ItS-type linear systems in the case of the state being partially observable. Above all, the Kalmam Bucy filtering of the dynamics is given by means of Girsanov transformation, by which the suboptimal feedback control of the LQ problem is determined. Furthermore, it is shown that the well-posedness of the LQ problem is equivalent to the solvability of a generalized differential Riccati equation （GDRE）.
