A New Contraction-Based NMPC Formulation Without Stability-Related terminal Constraints

TL;DR

This paper introduces a novel contraction-based NMPC formulation that guarantees stability without explicit contraction constraints, simplifying implementation and enhancing robustness against disturbances.

Contribution

It presents a new NMPC approach that avoids explicit contraction constraints, ensuring stability with milder assumptions and improved practical applicability.

Findings

Proves convergence of the closed-loop system.

Eliminates the need for multi-step control sequences.

Simplifies NMPC stability guarantees.

Abstract

Contraction-Based Nonlinear Model Predictive Control (NMPC) formulations are attractive because of the generally short prediction horizons they require and the needless use of terminal set computation that are commonly necessary to guarantee stability. However, the inclusion of the contraction constraint in the definition of the underlying optimization problem often leads to non standard features such as the need for multi-step open-loop application of control sequences or the use of multi-step memorization of the contraction level that may induce unfeasibility in presence of unexpected disturbance. This paper proposes a new formulation of contraction-based NMPC in which no contraction constraint is explicitly involved. Convergence of the resulting closed-loop behavior is proved under mild assumptions.