Distributed containment control for first-order and second-order multi-agent systems with delays and position-constraints.

This work addresses the discrete-time containment control problem for first-order and second-order systems, incorporating position constraints, nonuniform time delays, and switching topologies. Projection operators are introduced to maintain agent states within the position constraints. Then, model transformation methods, along with stochastic properties of matrices, are employed to handle coupled nonlinearities stemming from position constraints and time delays. By using local information, distributed projection-based control schemes are proposed for multi-agent systems. Theoretical analysis shows that all followers ultimately converge into the convex hull spanned by leaders if the union of the communication topologies contains a directed spanning tree within each specified time interval. Finally, the theoretical results are verified by numerical simulations.