Consensus for Second-Order Discrete-Time Agents With Position Constraints and Delays

This article addresses a consensus problem of second-order discrete-time agents in general directed networks with nonuniform position constraints, switching topologies, and communication delays. A projection operation is performed to ensure the agents stay in some given convex sets, and a distributed algorithm is employed for the consensus achievement of all agents. The analysis approach is to use a linear transformation to convert the original system into an equivalent system and then merge the nonlinear error term into the convex null of the agents' states so as to prove the consensus convergence of the system based on the properties of the non-negative matrices. It is shown that all agents finally converge to a consensus point while their positions stay in the corresponding constraint sets as long as the union of the communication graphs among each certain time interval is strongly connected even when the communication delays are considered. Finally, numerical simulation examples are given to show the theoretical results.