Compositional boundedness of solutions for symmetric nonautonomous control systems

Abstract—This paper presents boundedness results for symmetric nonautonomous control systems. The results are Lyapunov-based and exploit the symmetric structure present in many compositional or distributed control system. The work extends some of our prior work which defined an equivalence class of symmetric control systems by determining conditions for boundedness of solutions for such systems. The extension is along two lines. First, the prior work was focused on stability for autonomous symmetric systems, and this work extends it to the nonautonomous case. Second, the prior work required exact symmetry in the system whereas the results in this paper allow for symmetry-breaking in the nonautonomous terms, which significantly broadens the class of systems to which these results will apply. These results will be useful for robotics and control engineers dealing with large-scale and distributed systems which are composed of many similar components because it will enable closed-form analysis on a very small system, and then guarantee system properties for much larger equivalent systems. The application of the theoretical results is illustrated with a nonlinear consensus example. Other potential application areas would be, for example, the design of control algorithms for fleets of autonomous robotic vehicles acting in a coordinated manner. I