  This paper focuses on an online version of the emerging distributed
constrained aggregative optimization framework, which is particularly suited
for applications arising in cooperative robotics. Agents in a network want to
minimize the sum of local cost functions, each one depending both on a local
optimization variable, subject to a local constraint, and on an aggregated
version of all the variables (e.g., the mean). We focus on a challenging online
scenario in which the cost, the aggregation functions and the constraints can
all change over time, thus enlarging the class of captured applications.
Inspired by an existing scheme, we propose a distributed algorithm with
constant step size, named Projected Aggregative Tracking, to solve the online
optimization problem. We prove that the dynamic regret is bounded by a constant
term and a linear term related to time variations. Moreover, in the static case
(i.e., with constant cost and constraints), the solution estimates are proved
to converge with a linear rate to the optimal solution. Finally, numerical
examples show the efficacy of the proposed approach on a multi-robot basketball
game and a robotic surveillance scenario.
