Structural Controllability of Bilinear Systems on $\mathbb{SE(n)}$

TL;DR

This paper investigates the structural controllability of bilinear systems on the special Euclidean group using graph theory, introducing novel concepts like solid and broken edges to characterize controllability and accessibility.

Contribution

It develops a graph theoretic framework with new concepts to analyze and identify minimal control patterns for bilinear systems on (n).

Findings

Characterizes structural controllability using solid and broken edges.

Provides a method to identify the sparsest pattern for controllability.

Introduces the use of transitive closure in the analysis.

Abstract

Structural controllability challenges arise from imprecise system modeling and system interconnections in large scale systems. In this paper, we study structural control of bilinear systems on the special Euclidean group. We employ graph theoretic methods to analyze the structural controllability problem for driftless bilinear systems and structural accessibility for bilinear systems with drift. This facilitates the identification of a sparsest pattern necessary for achieving structural controllability and discerning redundant connections. To obtain a graph theoretic characterization of structural controllability and accessibility on the special Euclidean group, we introduce a novel idea of solid and broken edges on graphs; subsequently, we use the notion of transitive closure of graphs.