A general dynamic programming solution of discrete-time linear optimal control problems

An optimal control problem with linear dynamics and quadratic criterion is imbedded in a family of problems characterized by both initial and terminal points. The optimal value function is jointly quadratic in initial and terminal points, and the optimal control is jointly linear. Recursive formulas for the coefficients of these functions are developed. This generalized procedure can be used to solve several versions of the problem not solvable by the standard one-ended imbedding technique. In particular, a procedure doubling the number of stages at each iteration is given for problems with time-invariant coefficients.