Analysis of Unconstrained Nonlinear MPC Schemes with Time Varying Control Horizons

TL;DR

This paper derives a stability condition for unconstrained nonlinear model predictive control with time-varying control horizons, enabling the determination of prediction horizon lengths for guaranteed stability or performance.

Contribution

It introduces an analytical formula for stability conditions in nonlinear MPC without terminal constraints, including a sensitivity analysis for varying control horizons.

Findings

Derived a stability condition formula for nonlinear MPC

Provided a method to select prediction horizon lengths for stability

Analyzed the impact of time-varying control horizons

Abstract

For nonlinear discrete time systems satisfying a controllability condition, we present a stability condition for model predictive control without stabilizing terminal constraints or costs. The condition is given in terms of an analytical formula which can be employed in order to determine a prediction horizon length for which asymptotic stability or a performance guarantee is ensured. Based on this formula a sensitivity analysis with respect to the prediction and the possibly time varying control horizon is carried out.