Synthesis of Nonautonomous Systems with Specified Limit Cycles

This paper deals with a synthesis of a nonautonomous system with a stable limit cycle. By extending Green’s method, by which arbitrary periodic solutions can be designed in autonomous systems, it is shown that a nonautonomous system whose transient trajectories converge to a prescribed limit cycle can be synthesized. Furthermore, we apply receding horizon control to determine the optimal time-depending parameters in the system. The validity of the proposed synthesis is illustrated by examples of 3-dimensional systems.