Adaptive Networked Distributed Model Reference Control Systems with Strong Interconnections and Delays

The distributed control of a network of interconnected systems or agents based on a communication network for exchange of information has attracted considerable interest in research. Delays in the communicated information and the effect of strong interconnections between agents are two of the main challenges a distributed control system has to meet. In this paper we consider a linear Networked Distributed Control System (NDCS) that has strong interactions between its agents, as well as delays in the communication network. We assume that each agent knowns its own state, but receives information about its neighbors' states with some communication delay tau(ij). The control objective is to make each agent track efficiently a reference model by attenuating the effect of the strong interconnections via feedback based on the delayed state information. We prove that if the interconnections can be weakened enough and if the delays are smaller than some bounds which we present, then in the case of known interconnctions the proposed distributed control scheme can guarantee that the tracking error of each agent is bounded in respect to the delays and weakened interconnections, while in the case of unknown interconnections the proposed adaptive distributed control scheme can guarantee that the tracking error of each agent is bounded and small in the mean square sense in respect to the delays and weakened interconnections. Finally, we present an example to demonstrate the applicability and effectiveness of our scheme.