Time-Varying Containment Formation Control for Cooperative-Competitive Multi-Agent Networks Subject to Random Link Losses

This paper studies time-varying containment formation control for discrete-time multi-agent systems on structurally unbalanced signed networks subject to random link losses. Barycentric coordinates are used to translate a macroscopic formation specification into distributed spatial constraints, enabling leaders to steer followers into a moving convex hull. Communication failures are modeled by agent-level Bernoulli random variables: at each time step, a receiver either obtains all incoming messages or loses them, and leaders and followers may have different reception probabilities. Under structural unbalance and random link losses, topological and algebraic sufficient conditions are derived to ensure that cooperative weights dominate competitive ones. Convergence of the expected error is established through row-sum analysis of products of expected non-negative matrices. The results show that the followers enter the time-varying convex hull of the leaders despite random link losses and competitive interactions. Numerical simulations verify the effectiveness and robustness of the proposed protocol.