This work considers various families of quantum control landscapes (i.e. objective functions for optimal control) for obtaining target unitary transformations as the general solution of the controlled Schrodinger equation. We examine the critical point structure of the kinematic landscapes J(F) (U) = vertical bar vertical bar(U - W)A vertical bar vertical bar(2) and J(P)(U) = vertical bar vertical bar A vertical bar vertical bar(4) -vertical bar Tr(AA dagger W dagger U)vertical bar(2) defined on the unitary group U(H) of a finite-dimensional Hilbert space H. The parameter operator A is an element of B(H) is allowed to be completely arbitrary, yielding an objective function that measures the difference in the actions of U and the target W on a subspace of state space, namely the column space of A. The analysis of this function includes a description of the structure of the critical sets of these kinematic landscapes and characterization of the critical points as maxima, minima, and saddles. In addition, we consider the question of whether these landscapes are Morse Bott functions on U(H). Landscapes based on the intrinsic (geodesic) distance on U(H) and the projective unitary group P U(H) are also considered. These results are then used to deduce properties of the critical set of the corresponding dynamical landscapes.