A barrier function approach to constrained Pontryagin-based Nonlinear Model Predictive Control

TL;DR

This paper introduces a novel Pontryagin-based nonlinear model predictive control method that uses barrier functions to handle state constraints, ensuring stability and effectiveness without major algorithm modifications.

Contribution

The proposed approach uniquely integrates barrier functions into Pontryagin-based NMPC to manage nonlinear constraints without altering the core optimization algorithm.

Findings

Successfully applied to Lotka-Volterra system

Ensures stability via Lyapunov function analysis

Handles nonlinear constraints effectively

Abstract

A Pontryagin-based approach to solve a class of constrained Nonlinear Model Predictive Control problems is proposed which employs the method of barrier functions for dealing with the state constraints. Unlike the existing works in literature the proposed method is able to cope with nonlinear input and state constraints without any significant modification of the optimization algorithm. A stability analysis of the closed-loop system is carried out by using the L-2 norm of the predicted state tracking error as a Lyapunov function. Theoretical results are tested and confirmed by numerical simulations on the Lotka-Volterra prey/predator system.