Discrete linear optimal control systems with essentially quadratic cost functionals

This paper considers the optimal control problem of discrete linear systems with essentially quadratic cost functionals. Both closed target set and free endpoint problems are considered. Also, both bounded and unbounded controllers are considered. It is shown that Pontryagin's maximum principle is not only necessary but also sufficient for a number of cases. The existence and the uniqueness of the optimal controller are proved. This optimal control problem of discrete systems has been studied by many people. However, most of the previous results are concerned with the case of unbounded controllers. This paper presents a more unified method of studying such problems in the sense that basically the same geometrical approach is applied to both bounded and unbounded controllers.