Mesh refinement for event-triggered nonlinear model predictive control

Abstract

We consider the effect of using approximate system predictions in event-triggered control schemes. Such approximations often result from numerical transcription methods for solving continuous-time optimal control problems. Mesh refinement schemes guarantee upper bounds on the error in the differential equations used to model system dynamics. In particular, we show that with the accuracy guarantees of a mesh refinement scheme, then event-triggering schemes based on bounding the difference between predicted and measured state can be used with a guaranteed strictly positive inter-update time. We determine a lower bound for this time and show that additional knowledge of the employed transcription method and evaluation of the approximation errors may be used to obtain better online estimates of inter-update times. This is the first work to consider using the solution accuracy of an optimal control problem as a metric for triggering new control updates.