Linear quadratic regulation for discrete-time stochastic systems with input delay

This paper considers the stochastic LQR problem for systems with input delay and stochastic parameter uncertainties in the state and input matrices. The key to our approach is to covert the LQR control problem into an optimization problem in a Hilbert space for an associated backward stochastic model and give the optimal solution by exploiting the dynamic programming approach. Our solution is given in terms of two generalized Riccati difference equations (RDEs) of the same dimension as that of the plant.