Shear flow of viscoelastic fluids as a control problem

We consider a homogeneous parallel shear flow of a viscoelastic fluid with a single relaxation time. This problem results in a set of ordinary differential equations for the stresses. In this system, we view the shear rate as a control and consider the problem of steering the system to a given state of stress. For several popular constitutive models, we characterize the stresses which can be reached.