  In this paper we deal with distributed optimal control for nonlinear
dynamical systems over graph, that is large-scale systems in which the dynamics
of each subsystem depends on neighboring states only. Starting from a previous
work in which we designed a partially distributed solution based on a cloud,
here we propose a fully-distributed algorithm. The key novelty of the approach
in this paper is the design of a sparse controller to stabilize trajectories of
the nonlinear system at each iteration of the distributed algorithm. The
proposed controller is based on the design of a stabilizing controller for
polytopic Linear Parameter Varying (LPV) systems satisfying nonconvex sparsity
constraints. Thanks to a suitable choice of vertex matrices and to an iterative
procedure using convex approximations of the nonconvex matrix problem, we are
able to design a controller in which each agent can locally compute the
feedback gains at each iteration by simply combining coefficients of some
vertex matrices that can be pre-computed offline. We show the effectiveness of
the strategy on simulations performed on a multi-agent formation control
problem.
