Cooperative Control of Multiple Agents with Unknown High-frequency Gain Signs under Unbalanced and Switching Topologies

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.