  The paper considers pseudo-differential boundary value control systems. The
underlying operators form an algebra D with the help of which we are able to
formulate typical boundary value control problems. The symbolic calculus gives
tools to form e.g. compositions, formal adjoints, generalized right or left
inverses and compatibility conditions. By a parametrizability we mean that for
a given control system Au=0 one finds an operator S such that Au=0 if and only
if u=Sf. The computation rules of D (or its appropriate subalgebra D')
guarantee that in many applications S can be refinely analyzed or even
explicitly calculated. We outline some methods of homological algebra for the
study of parametrization S. Especially the projectivity of a certain factor
module (defined by the system equations) implies the parametrizability. We give
some examples to illustrate our computational methods.
