Finite-horizon indefinite optimal control for itô stochastic system with input delay

This paper is concerned with an indefinite stochastic linear quadratic control problem for Itô system with input delay in finite time horizon. An constrained differential Riccati equation is introduced. Furthermore, we obtain that the existence of the delayed optimal control is equivalent to the solvability of the constrained differential Riccati equation. An example is presented to illustrate the result established.