  Self-triggered control (STC) is a sample-and-hold control method aimed at
reducing communications within networked-control systems; however, existing STC
mechanisms often maximize how late the next sample is, and as such they do not
provide any sampling optimality in the long-term. In this work, we devise a
method to construct self-triggered policies that provide near-maximal average
inter-sample time (AIST) while respecting given control performance
constraints. To achieve this, we rely on finite-state abstractions of a
reference event-triggered control, in which early triggers are also allowed.
These early triggers constitute controllable actions of the abstraction, for
which an AIST-maximizing strategy can be computed by solving a mean-payoff
game. We provide optimality bounds, and how to further improve them through
abstraction refinement techniques.
