Linear Quadratic Optimal Control Problem for Linear Stochastic Generalized System in Hilbert Spaces

Zhaoqiang Ge ()
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Zhaoqiang Ge: School of Mathematics and Statistics, Xi’an Jiaotong University, No. 28, Xianning West Road, Xi’an 710049, China

Mathematics, 2022, vol. 10, issue 17, 1-20

Abstract: A finite-horizon linear stochastic quadratic optimal control problem is investigated by the GE-evolution operator in the sense of the mild solution in Hilbert spaces. We assume that the coefficient operator of the differential term is a bounded linear operator and that the state and input operators are time-varying in the dynamic equation of the problem. Optimal state feedback along with the well-posedness of the generalized Riccati equation is obtained for the finite-horizon case. The results are also applicable to the linear quadratic optimal control problem of ordinary time-varying linear stochastic systems.

Keywords: linear stochastic quadratic problem; linear stochastic generalized systems; optimal state feedback; GE-evolution operator; Hilbert spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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