Stochastic Linear Quadratic Optimal Control Problems for Stochastic Evolution Equations with Unbounded Control Operator

Abstract

The author studies a stochastic linear quadratic (SLQ for short) optimal control problem for systems governed by stochastic evolution equations, where the control operator in the drift term may be unbounded. Under the condition that the cost functional is uniformly convex, the well-posedness of the operator-valued Riccati equation is proved. Based on that, the optimal feedback control of the control problem is given.

Keywords

Stochastic evolution equation / Stochastic linear quadratic control problem / Optimal feedback control / Unbounded control operator / 93E20 / 49N10 / 93B52

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