PdI Regulation for Consensus: Application to Unknown Pure-Feedback Agents With State and Communication Delays

A novel proportional and delayed integral (PdI) transformation is proposed that recasts the cooperative control problem with communication delay to a simpler regulation problem. The PdI transformation enables the use of classical control techniques for solving leaderless consensus problems. Following this approach, we address for the first time the problem of leaderless consensus of heterogeneous multiagent systems in unknown pure-feedback form with state and communication time-delays and unknown disturbances. A general form of state delays is studied, which includes time-varying and distributed state delays among others. Retarded functional differential equations formalism is adopted in order to allow agent dynamics with such general state delays. The proposed algorithm guarantees that all closed-loop signals remain uniformly bounded and that the multiagent system achieves approximate consensus with prescribed steady-state error. Numerical simulations on a swarm of unmanned aerial vehicles verify the validity of the theoretical analysis.