A proposal on centralised and distributed optimisation via proportional-integral-derivative controllers (PID) control perspective

Motivated by the excellent performance of proportional-integral-derivative controllers (PIDs) in the field of control, the authors injected the philosophy of PID into optimisation and introduced two types of novel PID optimisers from a continuous-time view, which benefit from the idea that discrete-time optimisation algorithm can be modelled as a continuous dynamical system/controlled system. For centralised optimisation, the authors discuss the idea of the first-order PID optimiser and the second-order accelerated PID optimiser. Furthermore, this framework is extended into distributed optimisation settings, and a distributed PID optimiser is proposed. Finally, some numerical examples are given to verify our ideas.