Optimal control for Ito-stochastic systems with multiple input and output delays

This study is focused on the quadratic optimal control problem with partial information for the Ito-stochastic systems with multiple delayed inputs and outputs. Stochastic analysis and calculus of Ito-type stochastic variables are the main tools for the analysis and design. Applying a cost-value function, solvable conditions of the problem are provided and a new linear least-mean-square estimation problem, which is caused by the original problem, is also established. Through solving stochastic equations using the non-singularity of transition matrices, observations with free delays are obtained, then an optimal solution of the linear least-mean-square estimation problem is presented. Based on a couple of stochastic Riccati equations associated to estimation(filter) and control problems, an explicit and analytical output-feedback controller develop. The key technique is to pursue the felicitous value function to rebuild the new estimation problem and derive the controller via the interplay between the original problem and the filtering problem.