Successive method for general multiple linear-quadratic control problem indiscrete time

A successive method is proposed in this note for the general multiple linea r-quadratic control problem in discrete time. A family of auxiliary paramet ric linear-quadratic control problems is constructed such that its solution sequence converges to the optimal solution of the original problem. Theore tical analysis for the computational procedure and global convergence of th e successive method is provided. The successive method utilizes the special structure of the problem, thus being computationally efficient and being a ble to furnish a closed-loop optimal control law.