Discrete-time indefinite LQ control with state and control dependent noises

Abstract

This paper deals with the discrete-time stochastic LQ problem involving state and control dependent noises, whereas the weighting matrices in the cost function are allowed to be indefinite. We show that the well-posedness and the attainability of the LQ problem are equivalent. Furthermore, the set of all optimal controls is identified in terms of the solution to a generalized difference Riccati equation.