Linear-quadratic stochastic optimal control problem with incomplete information and uncertain noise statistics

We consider the problem of minimax-robust linear-quadratic control of multivariate non-stationary systems described by linear stochastic differential equations with uncertain noise intensities. The complete solution of the minimax control problem is achieved by means of the duality optimization techniques. We present the minimax control process in the explicit analytical form: its equations depend only on the dual problem solution, which can be obtained before the observations processing. For finding the dual solution (i.e., the least favorable intensity matrix) we propose an iterative algorithm proved to be convergent. To illustrate the analytical results, the specific numerical example is considered in detail