Decentralized Implementation of Centralized Controllers for Interconnected Systems

Given a centralized controller associated with a linear time-invariant interconnected system, this paper is concerned with designing a parameterized decentralized controller such that the state and input of the system under the obtained decentralized controller can become arbitrarily close to those of the system under the given centralized controller, by tuning the controller's parameters. To this end, a two-level decentralized controller is designed, where the upper level captures the dynamics of the centralized closed-loop system, and the lower level is an observed-based sub-controller designed based on the new notion of structural initial value observability. The proposed method can decentralize every generic centralized controller, provided the interconnected system satisfies very mild conditions. The efficacy of this work is elucidated by some numerical examples

A discussion on leading renormalon in the pole mass

Perturbative series of some quantities in quantum field theories, such as the pole mass of a quark, suffer from a kind of divergence called renormalon divergence. In this paper, the leading renormalon in the pole mass is investigated, and a map is introduced to suppress this renormalon. The inverse of the map is then used to generate the leading renormalon and obtain an expression to calculate its overall normalization. Finally, the overall normalization of the leading renormalon of the pole mass is calculated for several values of quark flavors.Comment: The published version; speculations about higher order renormalons are remove