Adaptation of Parameters in Heterogeneous Multi-agent Systems

This paper proposes an adaptation mechanism for heterogeneous multi-agent systems to align the agents' internal parameters, based on enforced consensus through strong couplings. Unlike homogeneous systems, where exact consensus is attainable, the heterogeneity in node dynamics precludes perfect synchronization. Nonetheless, previous work has demonstrated that strong coupling can induce approximate consensus, whereby the agents exhibit emergent collective behavior governed by the so-called blended dynamics. Building on this observation, we introduce an adaptation law that gradually aligns the internal parameters of agents without requiring direct parameter communication. The proposed method reuses the same coupling signal employed for state synchronization, which may result in a biologically or sociologically plausible adaptation process. Under a persistent excitation condition, we prove that the linearly parametrized vector fields of the agents converge to each other, thereby making the dynamics asymptotically homogeneous, and leading to exact consensus of the state variables.