Isochronous manifolds in self-triggered control

Feedback control laws are predominantly implemented on digital platforms as periodic tasks. Although periodicity simplifies the analysis and design of the implementation, new applications call for more efficient utilization of available resources such as processor utilization. To address this issue, new implementation paradigms, such as event-triggered and self-triggered control, have recently been proposed. These policies allow for a dynamic allocation of resources, since the execution times of the control task are defined according to the current state of the system. In this paper we continue our exploratory journey in the field of self-triggered control for nonlinear systems. In our previous work, we exploited the geometry of homogeneous and polynomial control systems to identify one dimensional manifolds along which the execution times scaled in a predictable manner. In this paper we complement our previous work by focusing on manifolds where the times remain constant. By merging both ideas new self-trigger conditions are derived, outperforming existing techniques.