Robust consensus-seeking via a multi-player nonzero-sum differential game

Considering a class of linear multi-agent systems, we study the problem of consensus-seeking in the presence of an exogenous signal, possibly representing a disturbance. We formulate the robust consensus-seeking problem as a nonzero-sum differential game. Exact solutions are characterized by a system of coupled differential Riccati equations (in the finite-horizon case) or algebraic Riccati equations (in the infinite-horizon case), whereas approximate solutions are characterized in terms of coupled matrix inequalites. Simulations for two examples are presented to illustrate the resulting performances: one example concerns consensus among agents described by single-integrator dynamics and the other concerns formation flight of unmanned aerial vehicles.