  Existing results on cooperative control of multi-agent systems with unknown
control directions require that the underlying topology is either fixed with a
strongly connected graph or switching between different strongly connected
graphs. Furthermore, in most cases the graph is assumed to be balanced. This
paper proposes a new class of nonlinear PI based algorithms to relax these
requirements and allow for unbalanced and switching topologies having a jointly
strongly connected basis. This is made possible for single-integrator (SI) and
double-integrator (DI) agents with non-identical unknown control directions by
a suitable selection of the distributed nonlinear PI functions. Moreover, as a
special case, the proposed algorithms are applied to strongly connected and
fixed graphs. Finally, simulation examples are given to show the validity of
our theoretical results.
