Linear quadratic optimal control problem for stochastic evolution equations with terminal state constraints in infinite dimensions
In 1968,Wonham proposed the stochastic linear quadratic optimal control problem.Subse-quently,in 1976 Bismut began to study the stochastic linear quadratic optimal control problems with random coefficients.Until 1998,Chen,Li,and Zhou successfully solved the stochastic linear quadratic optimal con-trol problem with indefinite control weight costs for the first time.Since then,more and more researchers have become interested in stochastic linear quadratic optimal control problems.In the past two decades,people have gradually begun to study the linear quadratic optimal control problem of infinite dimensional sto-chastic evolution equations as control systems.On the other hand,the state variables of control systems in practical applications often need to meet some constraint conditions.In this context,we investigate the linear quadratic optimal control problem of stochastic evolution equations with terminal state constrains.Based on the solvability of operator-valued Riccati equations,appropriate controllability of control systems and La-grangian duality theory,we obtain the expression for the optimal control of the constrained problem.
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