Consensus of Saturated Multi-Agent Systems: Tolerance to Non-Identical Asymmetric Saturation Levels

This paper explores the input saturation effect with non-identical asymmetric levels in the multi-agent consensus over a switching directed topology of weak connectivity. In particular, the saturation level for each agent is not symmetric, while the saturation levels associated with distinct agents are non-identical. Both the continuous- and discrete-time cases are considered. For both the saturated multi-agent systems, it is proven with the nonlinear contraction analysis that the conventional distributed protocols are sufficient for the achievement of the consensus given a uniformly jointly strongly connected topology condition, which does not require persistent connectivity. This thus confirms the tolerance of the multi-agent consensus to generic input saturation constraints with the non-identical asymmetric levels. Simulations are shown to confirm the established consensus results.