Fault-Tolerance of Control Systems with Dihedral Group Symmetry

Abstract

This paper deals with the fault-tolerance of systems that are symmetric with respect to the dihedral group D_m. The group D_m generally represents the geometric symmetry of a regular m-gon. We reveal the underlying mathematical mechanism of the loss of controllability for D_m-symmetric systems induced by failures and derive a necessary and sufficient condition to retain the controllability despite a failure. Moreover, we show the minimum number of functioning modules needed to retain the controllability despite the failures. It serves for a quantitative evaulation of fault-tolerance.