Monotonic Logical Time for Cooperative Tracking in Decentralized Multi-Agent Networks

Abstract

Cooperative target tracking in decentralized networks depends on a shared notion of time. We advocate monotonic logical time—a network-computed time function that all agents agree on and that never regresses—as a coordination primitive for distributed estimation in lossy, asymmetric wireless networks at the edge, where a hierarchical grandmaster is a single point of failure. The primitive is maintained by SoftMax consensus on the agents’ scalar logical-time functions, driven by a PI controller, with a drift-resilient extension—a smooth dead-zoned restoring force (Leaky DeadZone)— that counteracts the accumulation caused by the systematic deficit induced by asymmetric delays, characterized by a distribution-free lemma. Mean-square convergence is established for a push-based broadcast-gossip protocol with an explicit steady-state bound whose network-size dependence, for a fixed topology, is expressed through the push diameter; the construction enforces monotonicity (non-decreasing) of the agreed time function as a first-class invariant at every event, in contrast to average-consensus clock protocols whose monotonicity holds only asymptotically. These theoretical results are corroborated in simulation, and the algorithm’s feasibility is further demonstrated in small-scale hardware experiments. The synchronization layer is then used effectively in a downstream multi-target tracking task through a Time-Aware Local Voting Protocol (TA-LVP) operator.