Solving Problems of Minimization of Norms in a Finite Time Interval Using the Problem of Moments

Abstract

We consider the problem of minimizing the value of in the time interval    in the field     . Let   be given. Let`s consider the problem of minimizing the value of  with the restriction of the control norm  in the field  and the value of . In this case, the quantitiy  defined by equations (1) or (2) in the previous section can be called a function of  , that is   . Then the minimum value of   is the smallest real non-negative value of  and at this value.