Formation and trajectory tracking of discrete-time multi-agent systems using block control

The design of a decentralized discrete-time block control scheme, for a multi-agent system with a fixed topology, to achieve formation and trajectory tracking is proposed in this work. Each agent dynamics is represented either by a first-order or second-order discrete-time system, only the position of each agent´s neighbors is measured and their velocity and acceleration are unknown, and exclusively the agents that are connected to the virtual agent have full information of the reference. Each agent is provided with discrete-time state observers for the velocity and acceleration of its neighbors. It is proved that formation and trajectory tracking can be achieved applying the proposed block control with a consensus scheme. The stability of the controlled system with the state observer is proved.