Optimal control of quasi-linear systems of the diffusion type under incomplete information on the state

The problem of optimal control for a stochastic state-linear control system with coefficients of diffusion depending on the vector of state and control with quadratic criterion of the control quality is investigated. We assume that only a part of components of the state vector of the system are measured. On the basis of the Lyapunov-Lagrange method, we propose a method for searching for an optimal control strategy depending on known components of the state vector. The problem of synthesis of a control is reduced to solving a boundary-value problem for a system of ordinary differential equations of the Riccati type. Several model examples with different awareness about the system state are analyzed.