  The eigenvalue spectrum of the adjacency matrix of a network is closely
related to the behavior of many dynamical processes run over the network. In
the field of robotics, this spectrum has important implications in many
problems that require some form of distributed coordination within a team of
robots. In this paper, we propose a continuous-time control scheme that
modifies the structure of a position-dependent network of mobile robots so that
it achieves a desired set of adjacency eigenvalues. For this, we employ a novel
abstraction of the eigenvalue spectrum by means of the adjacency matrix
spectral moments. Since the eigenvalue spectrum is uniquely determined by its
spectral moments, this abstraction provides a way to indirectly control the
eigenvalues of the network. Our construction is based on artificial potentials
that capture the distance of the network's spectral moments to their desired
values. Minimization of these potentials is via a gradient descent closed-loop
system that, under certain convexity assumptions, ensures convergence of the
network topology to one with the desired set of moments and, therefore,
eigenvalues. We illustrate our approach in nontrivial computer simulations.
