The linear-quadratic problem for hereditary differential systems with targets in M2

The problem to be investigated in this paper is one of controlling a linear hereditary differential system to a fixed function target at a specified time while minimizing a quadratic cost functional. A solution to this problem as well as conditions which determine the interpretation of the optimal solution are found as a consequence of the abstract approach used. These conditions are unobtainable by approaches which do not exploit this abstract method of analysis. The results that are obtained are applied to related linear-quadratic optimal control problems. The problems considered are those which require that the system be driven to a fixed point in Euclidean n-space or to a fixed hyperplane in a function space.