An optimal control problem for a class of nonlinear hereditary systems

The paper is motivated by a finite interval, terminal constraint control problem for a class of nonlinear hereditary systems. Application of variational methods to the optimization problem requires a density condition (dense range) for some related linear hereditary systems, a controllability condition. The density condition can be characterized by a condition on the matrix representation of the differential of the input/output operator. The characterization reduces to a ´checkable´ condition when the matrix representation is time invariant.