Reducing the Prediction Horizon in NMPC: An Algorithm Based Approach

TL;DR

This paper introduces algorithms that enable stable nonlinear model predictive control with shorter prediction horizons by using multiple control steps and Lyapunov-based stability guarantees.

Contribution

It develops two novel algorithms and a stability theorem that allow for reduced prediction horizons in NMPC without sacrificing stability or performance.

Findings

Algorithms achieve stability with shorter horizons

Stability guarantees are based on Lyapunov arguments

Enhanced robustness in control feedback loops

Abstract

In order to guarantee stability, known results for MPC without additional terminal costs or endpoint constraints often require rather large prediction horizons. Still, stable behavior of closed loop solutions can often be observed even for shorter horizons. Here, we make use of the recent observation that stability can be guaranteed for smaller prediction horizons via Lyapunov arguments if more than only the first control is implemented. Since such a procedure may be harmful in terms of robustness, we derive conditions which allow to increase the rate at which state measurements are used for feedback while maintaining stability and desired performance specifications. Our main contribution consists in developing two algorithms based on the deduced conditions and a corresponding stability theorem which ensures asymptotic stability for the MPC closed loop for significantly shorter prediction horizons.