Inaccuracy matters: accounting for solution accuracy in event-triggered nonlinear model predictive control

TL;DR

This paper investigates how solution accuracy impacts event-triggered nonlinear model predictive control, proposing methods to incorporate approximation errors for guaranteed inter-update times and constraint satisfaction.

Contribution

It introduces the first approach to include prediction accuracy in triggering metrics for nonlinear MPC, enhancing reliability and constraint handling.

Findings

Guaranteed positive inter-update times with mesh refinement

Improved online estimates of update intervals using approximation errors

Constraint tightening based on solution accuracy

Abstract

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.