Performance bounds for NMPC combined with Sensitivity Updates

TL;DR

This paper establishes stability bounds for NMPC without terminal constraints using sensitivity updates, demonstrating improved performance in a halfcar example through Lipschitz conditions and relaxed Lyapunov arguments.

Contribution

It introduces a stability proof for NMPC without terminal constraints employing sensitivity updates, expanding theoretical understanding and practical application of disturbance handling.

Findings

Stability of NMPC without terminal constraints is achievable with sensitivity updates.

Lipschitz conditions are satisfied through sensitivity analysis along the closed loop.

Performance improvements are demonstrated in a halfcar example, enhancing comfort and handling.

Abstract

In this paper we present a stability proof of model predictive control without stabilizing terminal constraints of cost which are subject to unknown but measurable disturbances. To this end, a relaxed Lyapunov argument on the nominal system and Lipschitz conditions on the open loop change of the optimal value function and the stage costs are employed. Based on the special case of sensitivity analysis, we show that Lipschitz assumptions are satisfied if a sensitivity update can be performed along the closed loop solution. To illustrate our approach we present a halfcar example and show performance improvement of the updated solution with respect to comfort and handling properties.