  Doubly curved thin concrete shells are very efficient building structures,
suitable for light-weight construction because of their high structural
stability. In the process of constructing such shells, an efficient innovative
flexible formwork that is based on a cable network can be used instead of the
costly conventional timber formwork. To guarantee the structural properties of
such a shell, the desired form, that is designed and optimized in advance,
needs to be precisely achieved. The sensitivity of the flexible cable net
formwork to fabrication tolerances and uncertainties makes high accuracy
challenging. We propose a new construction method where the form of the cable
net structure is measured and controlled in a feedback loop during its
construction. Two models based on a force and on an energy approach are
reviewed and their equivalence is shown. An efficient control algorithm, which
is based on a variant of Sequential Quadratic Programming, and which guarantees
feasibility at every iteration, is derived. Based on mild assumptions on the
cable net, global convergence to a stationary point is shown. For practical
applicability, an extension of the control algorithm for computing sparse input
vectors is given. Experimental results on a cable net formwork prototype for a
shell roof structure are presented to demonstrate the control performance.
