Inaccuracy Matters: Accounting for Solution Accuracy in Event-Triggered Nonlinear Model Predictive Control

We consider the effect of using approximate system predictions in event-triggered control schemes. These approximations often 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 that model the system dynamics. We employ the accuracy guarantees of a mesh refinement scheme to show that the proposed event-triggering scheme, which compares the measured system with approximate state predictions, can be used with a guaranteed strictly positive interupdate time. Furthermore, if knowledge of the employed transcription scheme or the approximation errors are available, then better online estimates of interupdate times can be obtained. We also detail a method of tightening constraints on the approximate system trajectory to guarantee constraint satisfaction of the continuous-time system. This is the first work to incorporate prediction accuracy in triggering metrics to guarantee reliable lower bounds for interupdate times and perform solution-dependent constraint tightening.