Spatio-Temporal Symmetries in Control Systems: An Application to Formation Control

Abstract With the aim of addressing the stabilization problem of periodic trajectories in systems composed of identical interconnected subsystems, we introduce the class of “spatio-temporally symmetric” nonlinear systems. We address in detail the linear, time-varying case and present conditions for the synthesis of a static and a dynamic stabilizing controller. We show that linear spatio-temporally symmetric systems can be reduced to hybrid systems, described by a periodic linear system with periodic state jumps. As an application example, we present the stabilization of a formation of unicycle robots in cyclic pursuit.