A Carleman approximation scheme for a stochastic optimal control problem in the continuous-time framework

The paper investigates the optimal control problem for a stochastic linear differential system, driven by a persistent disturbance generated by a nonlinear stochastic exogenous system. The assumption of incomplete information has been assumed, that is neither the state of the system, nor the state of the exosystem are directly measurable. The standard quadratic cost functional has been considered. The approach followed consists of applying the Carleman approximation scheme to the exosystem, which provides a stochastic bilinear system. Then, the optimal regulator is obtained (i.e. the solution to the minimum control problem among all the affine transformations of the measurements). Better performances of the regulator are expected using higher order system approximations.