Performance Bounds for Multi-Vehicle Networks With Local Integrators

In this letter, we consider the problem of coordinating a collection of nth-order integrator systems. The coordination is achieved through the novel serial consensus design; this control design achieves a stable closed-loop system while adhering to the constraint of only using local and relative measurements. Earlier work has shown that second-order serial consensus can stabilize a collection of double integrators with scalable performance conditions independent of the number of agents and topology. This letter generalizes these performance results to an arbitrary order ${\mathrm { n}}\geq 1$ . The derived performance bounds depend on the condition number, measured in the vector-induced maximum matrix norm, of a general diagonalizing matrix. We precisely characterize how a minimal condition number can be achieved. Third-order serial consensus is illustrated through a case study of PI-controlled vehicular formation, where the added integrators are used to mitigate the effect of unmeasured load disturbances. The theoretical results are illustrated through examples.