Exponential Bipartite Containment Tracking over Multi-leader Coopetition Networks

This paper addresses the distributed bipartite containment tracking-control problem for autonomous vehicles steered by multiple leaders. Some leaders are cooperative and others are competitive, so the vehicles form a so-called coopetition network; in which the interaction links may be negative or positive. The presence of cooperative and antagonistic leaders does not enable the system to achieve consensus. Instead, the followers' states converge to a residual compact set, not predefined, but depending only on the leaders' states. We establish global exponential stability for this so-called bipartite containment set, and we compute the exact equilibria to which all agents converge inside of it. Our proofs are constructive, that is, we provide strict Lyapunov functions, which also allow us to establish robustness with respect to external disturbances. Numerical simulations illustrate our theoretical findings.