Koopman-Based Linear MPC for Safe Control using Control Barrier Functions

TL;DR

This paper introduces a Koopman-based linear MPC framework that simplifies safety-critical control of nonlinear systems into a quadratic program, enabling real-time safe trajectory planning.

Contribution

It combines Koopman operator theory with control barrier functions to linearize nonlinear dynamics for efficient, safe model predictive control.

Findings

Successfully applied to robot navigation with nonlinear dynamics

Achieves real-time safe control through quadratic programming

Demonstrates improved computational efficiency over nonlinear MPC

Abstract

This paper proposes a Koopman-based linear model predictive control (LMPC) framework for safety-critical control of nonlinear discrete-time systems. Existing MPC formulations based on discrete-time control barrier functions (DCBFs) enforce safety through barrier constraints but typically result in computationally demanding nonlinear programming. To address this challenge, we construct a DCBF-augmented dynamical system and employ Koopman operator theory to lift the nonlinear dynamics into a higher-dimensional space where both the system dynamics and the barrier function admit a linear predictor representation. This enables the transformation of the nonlinear safety-constrained MPC problem into a quadratic program (QP). To improve feasibility while preserving safety, a relaxation mechanism with slack variables is introduced for the barrier constraints. The resulting approach combines the modeling capability of Koopman operators with the computational efficiency of QP. Numerical simulations on a navigation task for a robot with nonlinear dynamics demonstrate that the proposed framework achieves safe trajectory generation and efficient real-time control.