Discrete-Time Indefinite Stochastic Linear Quadratic Optimal Control with Second Moment Constraints

Abstract EN

This paper studies the discrete-time stochastic linear quadratic (LQ) problem with a second moment constraint on the terminal state, where the weighting matrices in the cost functional are allowed to be indefinite.

By means of the matrix Lagrange theorem, a new class of generalized difference Riccati equations (GDREs) is introduced.

It is shown that the well-posedness, and the attainability of the LQ problem and the solvability of the GDREs are equivalent to each other.