Stability and performance analysis of NMPC: Detectable stage costs and general terminal costs

TL;DR

This paper analyzes the stability and performance of nonlinear model predictive control (NMPC) with input constraints, focusing on detectable stage costs and general terminal costs, providing new theoretical bounds and practical insights.

Contribution

It introduces a stability and performance analysis framework for NMPC that handles positive semi-definite costs and general terminal costs, extending existing results.

Findings

Provides a prediction horizon length ensuring stability and performance bounds.

Applicable to positive semi-definite (detectable) cost functions.

Demonstrates practical relevance through numerical examples.

Abstract

We provide a stability and performance analysis for nonlinear model predictive control (NMPC) schemes subject to input constraints. Given an exponential stabilizability and detectability condition w.r.t. the employed state cost, we provide a sufficiently long prediction horizon to ensure asymptotic stability and a desired performance bound w.r.t. the infinite-horizon optimal controller. Compared to existing results, the provided analysis is applicable to positive semi-definite (detectable) cost functions, provides tight bounds using a linear programming analysis, and allows for a seamless integration of general positive-definite terminal cost functions in the analysis. The practical applicability of the derived theoretical results are demonstrated with numerical examples.