A finite-time distributed dynamic consensus protocol for tracking maximum (minimum) reference signals

Tracking the maximum or minimum of a set of signals is a fundamental task in multiple applications involving coordinated multi-agent systems. This work tackles the dynamic maximum or minimum consensus problem in networked multi-agent systems. Within this framework, every agent has access to a local exogenous signal, and the objective is to ensure that all agents track the time-varying maximum (minimum) signal of the exogenous signals by only relying on local information. We present a novel distributed protocol achieving this objective in finite time under undirected switching network topologies. The assumptions in our study pertain solely to the connectivity of the network topologies and the knowledge of the bounds on the derivatives of the exogenous signals. Numerical results with sinusoidal and piecewise linear signals corroborate the theoretical findings.