Proportional-Integral-Retarded (PIR) Protocol with Multiple Intentional Delays for Second-Order Multi-Agent Systems

We propose a delay-based controller called Proportional-Integral-Retarded (PIR) protocol with multiple intentional delays for second-order multi-agent systems. Compared with derivative-like controllers, the PIR protocol only relies on the position measurement and thus avoids the undesirable noise introduced by the derivative action. A free variable
$k$
, associated with the parameters of this protocol, is introduced such that the settling time can be adjusted not only by assigning the dominant root but also by choosing
$k$
. We then present a tuning strategy for this protocol by guaranteeing a desired exponential decay rate and a user-defined dominance index through the discriminant operation. Finally, we highlight that the network using the PIR protocol can attain fast consensus and then disclose the noise attenuation property of this protocol compared with a conventional Proportional-Integral-Derivative (PID) scheme.