Stability and Performance Guarantees for MPC Algorithms without Terminal Constraints

TL;DR

This paper introduces techniques to ensure stability and performance guarantees for MPC algorithms with shorter prediction horizons by relaxing Lyapunov inequalities, bridging the gap between theory and practice.

Contribution

It presents novel methods to establish stability and suboptimality for MPC without terminal constraints using relaxed Lyapunov inequalities.

Findings

Stability can be guaranteed with shorter prediction horizons.

Suboptimality estimates are improved using controllability-based structural properties.

The approach reduces computational complexity in MPC algorithms.

Abstract

A typical bottleneck of model predictive control algorithms is the computational burden in order to compute the receding horizon feedback law which is predominantly determined by the length of the prediction horizon. Based on a relaxed Lyapunov inequality we present techniques which allow us to show stability and suboptimality estimates for a reduced prediction horizon. In particular, the known structural properties of suboptimality estimates based on a controllability condition are used to cut the gap between theoretic stability results and numerical observations.