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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.

In this paper we present a novel strategy to compute minimum-time trajectories for quadrotors. In particular, we consider the motion in constrained environments, taking into account the physical limitations of the vehicle. Instead of approaching the optimization problem in its standard time-parameterized formulation, the proposed strategy is based on an appealing re-formulation. Transverse coordinates, expressing the distance from a "reference" path, are used to parameterize the vehicle position and a spatial parameter is used as independent variable. This re-formulation allows us to (i) obtain a fixed horizon problem and (ii) easily formulate (even complex) position constraints. The effectiveness of the proposed strategy is proven by numerical computations on two different illustrative scenarios.