  We consider the effect of using approximate system predictions in
event-triggered control schemes. Such approximations may result from using
numerical transcription methods for solving continuous-time optimal control
problems. Mesh refinement can guarantee upper bounds on the error in the
differential equations which model the system dynamics. With the accuracy
guarantees of a mesh refinement scheme, we show that the proposed
event-triggering scheme -- which compares the measured system with approximate
state predictions -- can be used with a guaranteed strictly positive
inter-update time. We show that if we have knowledge of the employed
transcription scheme or the approximation errors, then we can obtain better
online estimates of inter-update times. We additionally detail a method of
tightening constraints on the approximate system trajectory used in the
nonlinear programming problem to guarantee constraint satisfaction of the
continuous-time system. This is the first work to incorporate prediction
accuracy in triggering metrics. Using the solution accuracy we can guarantee
reliable lower bounds for inter-update times and perform solution dependent
constraint tightening.
