Optimal Control and Stabilization for Itô Systems with Input Delay

The paper considers the linear quadratic regulation (LQR) and stabilization problems for Ito stochastic systems with two input channels of which one has delay. underlying problem actually falls into field asymmetric information control because nonidentical measurability induced by In contrast single-channel single-delay problems, challenge under study lies in interaction between are measurable respect to different filtrations. key techniques conquering such difficulty maximum principle orthogonal decomposition reorganization technique proposed a companion paper. authors provide way solve delayed forward backward differential equation (D-FBSDE) arising from principle. necessary sufficient solvability condition optimal controller LQR given terms new Riccati established herein. Further, mean square sense is provided given. idea can be extended related multiple delays.