Retrofitting state feedback control of networked nonlinear systems based on hierarchical expansion

In this paper, we propose a systematic method to design retrofit controllers for networked nonlinear systems. The retrofit controller, which consists of a linear state feedback controller and a dynamical compensator, can improve the control performance for a subsystem of interest, while guaranteeing the stability of the whole closed-loop system. Towards the retrofit controller design, we introduce a type of state-space expansion, called hierarchical expansion. The cascade structure of the hierarchical expansion realization enables the systematic design of a stabilizing controller for a low-dimensional linear model extracted from the subsystem of interest. As a result, we can design a retrofit controller without explicit consideration of the dynamics of subsystems other than the subsystem of interest. The effectiveness of the proposed method is demonstrated through a power network example.