Stability Properties of the Adaptive Horizon Multi-Stage MPC

TL;DR

This paper introduces an adaptive horizon multi-stage MPC algorithm that ensures stability and feasibility while reducing computational costs through sensitivity analysis and terminal ingredients, demonstrated on numerical examples.

Contribution

It proposes a novel adaptive horizon approach for multi-stage MPC that minimizes the prediction horizon and computational effort while maintaining stability.

Findings

Reduces computational delay in multi-stage MPC

Ensures recursive feasibility and stability

Demonstrates effectiveness through numerical examples

Abstract

This paper presents an adaptive horizon multi-stage model-predictive control (MPC) algorithm. It establishes appropriate criteria for recursive feasibility and robust stability using the theory of input-to-state practical stability (ISpS). The proposed algorithm employs parametric nonlinear programming (NLP) sensitivity and terminal ingredients to determine the minimum stabilizing prediction horizon for all the scenarios considered in the subsequent iterations of the multi-stage MPC. This technique notably decreases the computational cost in nonlinear model-predictive control systems with uncertainty, as they involve solving large and complex optimization problems. The efficacy of the controller is illustrated using three numerical examples that illustrate a reduction in computational delay in multi-stage MPC.