On the accuracy of the model predictive control method

TL;DR

This paper analyzes the accuracy of Model Predictive Control (MPC) for Bolza problems, providing error estimates that account for inaccuracies in predictions and measurements, with specialized results for coercive and affine problems.

Contribution

It introduces a novel error estimation technique for MPC solutions, extending strong metric sub-regularity and a new control space metric, applicable to specific problem classes.

Findings

Provides error bounds for MPC solutions with inaccurate predictions.

Specializes results for coercive and affine problem classes.

Extends the notion of strong metric sub-regularity in control analysis.

Abstract

The paper investigates the accuracy of the Model Predictive Control (MPC) method for finding online approximate optimal feedback control for Bolza type problems on a fixed finite horizon. The predictions for the dynamics, the state measurements, and the solution of the auxiliary open-loop control problems that appear at every step of the MPC method may be inaccurate. The main result provides an error estimate of the MPC-generated solution compared with the optimal open-loop solution of the ``ideal'' problem, where all predictions and measurements are exact. The technique of proving the estimate involves an extension of the notion of strong metric sub-regularity of set-valued maps and utilization of a specific new metric in the control space, which makes the proof non-standard. The result is specialized for two problem classes: coercive problems, and affine problems.