Implementation of arbitrary periodic dynamic behaviors in networked systems

Decentralized control of networked systems has been widely investigated in the literature, with the aim of regulating the overall state of the system to some desired configuration, thus obtaining coordinated emerging behaviors (e.g. synchronization, swarming, coverage, formation control) by means of local interaction. In this paper we introduce a methodology to solve a tracking problem, that is defining a decentralized control strategy for making a networked system follow an arbitrarily defined periodic setpoint function. The most suitable interconnection topology is defined together with the control law as the solution of a constrained optimization problem, in order to ensure asymptotic tracking. Simulations are provided for validating the proposed control strategy.