Finite-Time Consensus Tracking of Multi-Agent Systems Using Time-Fuel Optimal Pursuit Evasion

Computation of a decentralized feedback strategy for consensus tracking problem of multi-agent systems that communicate over a directed graph containing a directed spanning tree, is considered. The agents are subjected to bounded control inputs and are governed by double integrator dynamics. Agents transmit their state measurement data and upper bound on control input to other agents over directed edges in the graph. Using the transmitted data, the agents track the reference trajectory generated by an agent that is assigned as the root node. Each pair of agents connected by a directed edge is identified as a pursuer-evader pair where the child node (pursuer) tries to match its state with that of the parent node (evader), in finite time by consuming min-max amount of time-fuel. Nash equilibrium feedback strategies using time-fuel optimal switching curves are derived for the two-player time-fuel pursuit evasion game. By making use of the derived Nash equilibrium strategy each child node tracks its respective parent node's state by locally consuming min-max time-fuel cost. As a consequence, all agents are shown to track the reference trajectory generated by the root agent in finite time with reduced fuel consumption.