"solution" .
"process" .
_:Nf45ca133778742169db8249669b85563 .
"stochastic differential equations" .
"system" .
.
_:Ne0ea74b2656a40e5b95e9915692a9ffc .
"stochastic systems" .
"In this paper, we consider the mixed optimal control of a linear stochastic system with a quadratic cost functional, with two controllers\u2014one can choose only deterministic time functions, called the deterministic controller, while the other can choose adapted random processes, called the random controller. The optimal control is shown to exist under suitable assumptions. The optimal control is characterized via a system of fully coupled forward-backward stochastic differential equations (FBSDEs) of mean-field type. We solve the FBSDEs via solutions of two (but decoupled) Riccati equations, and give the respective optimal feedback law for both deterministic and random controllers, using solutions of both Riccati equations. The optimal state satisfies a linear stochastic differential equation (SDE) of mean-field type. Both the singular and infinite time-horizonal cases are also addressed." .
_:N1e5283f12c424478ba53c098f04e5654 _:Ne0ea74b2656a40e5b95e9915692a9ffc .
_:N799202722d674e01aae3149b2341081b "10.1186/s41546-018-0035-x" .
"true"^^ .
.
"cost" .
.
"2019-01-04" .
"optimal state satisfies" .
"quadratic cost" .
_:N233586e3ebca40209814c913514e8860 .
.
_:N63b02446fb014649b7da318edf2a2b54 "1" .
.
"Mixed deterministic and random optimal control of linear stochastic systems with quadratic costs" .
"https://doi.org/10.1186/s41546-018-0035-x" .
_:Nf45ca133778742169db8249669b85563 "pub.1111105202" .
_:N63b02446fb014649b7da318edf2a2b54 .
_:N63b02446fb014649b7da318edf2a2b54 .
"Tang" .
"differential equations" .
"assumption" .
"2022-01-01T18:53" .
.
"feedback law" .
"equations" .
"controller" .
"respective optimal feedback law" .
"infinite time-horizonal cases" .
"American Institute of Mathematical Sciences (AIMS)" .
_:N799202722d674e01aae3149b2341081b "doi" .
.
"Department of Finance and Control Sciences, School of Mathematical Sciences, Fudan University, 200433, Shanghai, China" .
_:N233586e3ebca40209814c913514e8860 .
"FBSDEs" .
.
.
"Probability, Uncertainty and Quantitative Risk" .
.
.
_:N00d6cd870d204188b0c87335cea67349 "4" .
"Statistics" .
"backward stochastic differential equations" .
.
.
"random process" .
.
_:N00d6cd870d204188b0c87335cea67349 .
"satisfies" .
.
"cases" .
.
"deterministic controller" .
"deterministic time functions" .
_:Ne0ea74b2656a40e5b95e9915692a9ffc .
"Riccati equation" .
_:N799202722d674e01aae3149b2341081b .
"2019-01-04" .
_:N233586e3ebca40209814c913514e8860 "Springer Nature - SN SciGraph project" .
"en" .
"Hu" .
"mean-field type" .
"linear stochastic systems" .
_:N1e5283f12c424478ba53c098f04e5654 .
"2367-0126" .
"Mathematical Sciences" .
_:Nf45ca133778742169db8249669b85563 .
"time function" .
.
.
"article" .
"random controller" .
"paper" .
.
"Department of Finance and Control Sciences, School of Mathematical Sciences, Fudan University, 200433, Shanghai, China" .
.
"suitable assumptions" .
.
_:N1e5283f12c424478ba53c098f04e5654 .
.
"Shanjian" .
"Univ Rennes, CNRS, IRMAR - UMR 6625, 35000, Rennes, France" .
"law" .
"Ying" .
_:N799202722d674e01aae3149b2341081b .
"mixed optimal control" .
"2095-9672" .
.
"time-horizonal cases" .
"optimal feedback law" .
.
_:N00d6cd870d204188b0c87335cea67349 .
"state satisfies" .
"Applied Mathematics" .
.
"articles" .
.
"https://scigraph.springernature.com/explorer/license/" .
.
"random optimal control" .
"types" .
"function" .
.
.
"optimal control" .
_:Nf45ca133778742169db8249669b85563 "dimensions_id" .
"1" .
"linear stochastic differential equations" .