Least Controls for a Class of Constrained Linear Stochastic Systems

This paper introduces a class of constrained linear stochastic systems. The main objective is to investigate whether there exists a least control, in a sense that it exerts least effort in controlling the system to within a predetermined region. Our approach of finding a least control is: (a) to characterize a class of functional polyhedral sets of functions which have least elements, and (b) to construct a least-control process through these least elements. Existence of a least control is established. And the connection between a least control and a solution of the dynamic complementarity problem (DCP) is also discussed.