Performance bounds of adaptive MPC with bounded parameter uncertainties

TL;DR

This paper establishes a worst-case performance bound for a linear adaptive model predictive control scheme with bounded parameter uncertainties, enabling a priori evaluation of control performance considering initial errors and constraints.

Contribution

It introduces a novel a priori performance bound for adaptive MPC with bounded uncertainties, linking system errors and constraints to control performance.

Findings

Performance bound can be computed prior to control implementation.

The bound relates initial parameter error to overall control performance.

Numerical example illustrates the bound's applicability and accuracy.

Abstract

Model predictive control is a control approach that minimizes a stage cost over a predicted system trajectory based on a model of the system and is capable of handling state and input constraints. For uncertain models, robust or adaptive methods can be used. Because the system model is used to calculate the control law, the closed-loop behavior of the system and thus its performance, measured by the sum of the stage costs, are related to the model used. If it is adapted online, a performance bound is difficult to obtain and thus the impact of model adaptation is mostly unknown. This work provides a (worst-case) performance bound for a linear adaptive predictive control scheme with a specific model parameter estimation. The proposed bound is expressed in terms of quantities such as the initial system parameter error and the constraint set, among others and can be calculated a priori. The results are discussed in a numerical example.