On the applicability of the sweep method to optimal control problems

Two types of linear quadratic problems are investigated. The first is associated with problems in which the final time is specified and the second with problems in which the final time is given implicitly. McReynolds and Bryson [1] have presented a sweep method for solving linear quadratic problems. This technique generates a feedback control law. The applicability of this method depends on the existence of the inverse of a matrix and the finiteness of two other matrices. Conditions assuring these properties are presented. The results of Dreyfus [2] for the first type of linear quadratic problem are extended to problems of the second type. In addition, it is shown that there are two special cases of this problem for which the desired inverse exists at the final time. For these cases, only two matrix equations need to be solved rather than the three matrix equations for the general case.