TIME-VARYING SCALED CONSENSUS: DYNAMIC MANIFOLD CONVERGENCE UNDER HYBRID SCALING PROFILES

Abstract

This paper investigates the problem of time-varying scaled consensus in directedmulti-agent systems, where agent states evolve under nonuniform and time-dependent inu-ence. The core challenge lies in ensuring asymptotic synchronization of scaled states acrossa network with heterogeneous and dynamically evolving scaling functions. A distributedconsensus protocol is proposed that incorporates agent-specific time-varying scaling profiles, subject to mild regularity and boundedness conditions. By leveraging Lyapunov-basedanalysis and a vector-valued extension of Barbalats Lemma, we establish convergence ofthe scaled states to a common dynamic manifold. The framework is further extended toaccommodate global reference tracking on the evolving scaled-consensus manifold. Numeri-cal simulations validate the theoretical results and demonstrate robustness under both staticand time-varying scaling. The main innovation lies in unifying dynamic consensus and adap-tive scaling within a tractable analytical framework, enabling coordination in networks withasymmetric and time-dependent agent roles.