Application of Terminal Region Enlargement Approach for Discrete Time Quasi Infinite Horizon NMPC

TL;DR

This paper introduces scalable methods for enlarging the terminal region in discrete-time Quasi Infinite Horizon NMPC, significantly improving stability guarantees by using controller-based approaches with tunable parameters.

Contribution

It proposes novel arbitrary controller and LQR-based approaches that provide greater flexibility for terminal region enlargement in QIH-NMPC, applicable to systems of any size.

Findings

Terminal regions are approximately 10 times larger with proposed methods.

Approaches involve solving modified Lyapunov equations for terminal penalty.

Methods are demonstrated on a benchmark two-state system.

Abstract

Ensuring nominal asymptotic stability of the Non-linear Model Predictive Control (NMPC) controller is not trivial. Stabilizing ingredients such as terminal penalty term and terminal region are crucial in establishing the asymptotic stability. Approaches available in the literature provide limited degrees of freedom for the characterization of the terminal region for the discrete time Quasi Infinite Horizon NMPC (QIH-NMPC) formulation. Current work presents alternate approaches namely arbitrary controller based approach and LQR based approach, which provide large degrees of freedom for enlarging the terminal region. Both the approaches are scalable to system of any state and input dimension. Approach from the literature provides a scalar whereas proposed approaches provide a linear controller and two additive matrices as tuning parameters for shaping of the terminal region. Proposed approaches involve solving modified Lyapunov equations to compute terminal penalty term, followed by explicit characterization of the terminal region. Efficacy of the proposed approaches is demonstrated using benchmark two state system. Terminal region obtained using the arbitrary controller based approach and LQR based approach are approximately 10.4723 and 9.5055 times larger by area measure when compared to the largest terminal region obtained using the approach from the literature.