Lagrangian Formulation and Geometric Control of Switching LC Electrical Networks

Using Lagrangian formalism, switching electrical networks can be modeled as systems varying on Lie groups which evolve according to a finite number of vector fields. In particular, under appropriate assumptions, LC circuits can be modeled as systems on SO(n), The first goal of this report is to formalize the modeling of LC circuits as systems on SO(n) and give precise assumptions under which this is valid. In particular we give assumptions on the graph representing the network. Then, as an example of this formalism, we study controllability and give control algorithms for classes of switching electrical networks. The main ingredients in this analysis are controllability conditions from geometric control and techniques of Lie groups decompositions