On Networked Dynamical Systems with Heterogeneous Constraints: Equilibrium Points and Stability

In this paper, we investigate multi-agent systems with heterogeneous constraints, which can represent the heuristic beliefs of the agents towards an issue or the physical constraints of the agents. One typical example is a group of interacting unmanned aerial vehicles in a complex environment with multiple physical constraints. As a result of the heterogeneity of the constraints, an equilibrium point may not exist and is presumably to be a dissensus point when it exists. We investigate the existence of equilibrium points from the perspective of Kakutani's fixed point theory for a set-valued map. We also prove the local/global stability of certain equilibrium points. Then, a special case that the constraints are homogeneous is taken into account. The constrains are assumed to take interval forms with nonempty intersection. It is proved that consensus can be achieved globally and asymptotically for this case. Numerical examples are designed to illustrate our theoretical findings.