Discrete-time indefinite stochastic linear quadratic optimal control with equality constraints

This paper studies the discrete-time indefinite stochastic linear quadratic optimal control problem with the equality terminal state constraints,which can be transformed into a mathematical programming with equality constraints. By means of matrix Lagrange theorem, a necessary condition for the existence of optimal linear state feedback control is given. The previous results on discrete-time stochastic linear quadratic optimal control without constraints, can be viewed as corollaries of the main theorem of this paper.