An apologia for stabilising terminal conditions in model predictive control

Abstract

This paper defends the use of a terminal cost and an explicit or implicit terminal constraint for ensuring the stability of model predictive control systems. Existing methods for ensuring stability are briefly reviewed. The necessity of a terminal constraint to satisfy certain design requirements is established. The advantages and disadvantages of employing terminal stabilising conditions are discussed.

Keywords:

• terminal cost
• terminal constraint set
• closed loop stability
• model predictive control

Acknowledgements

The author would like to thank Professor J.B. Rawlings for many helpful discussions.

Notes

1. The constraint is infinite dimensional

2. Yu’s proof requires some revision