Koopman-BoxQP: Solving Large-Scale NMPC at kHz Rates

TL;DR

This paper introduces Koopman-BoxQP, a novel framework that combines Koopman modeling and structured quadratic programming to enable real-time large-scale NMPC solutions at kilohertz rates on standard processors.

Contribution

It presents a new approach that learns a linear Koopman model, simplifies the prediction to a structured BoxQP, and develops a specialized solver for fast NMPC computation.

Findings

Successfully solves large-scale NMPC with 1040 variables and 2080 inequalities at kHz rates.

Demonstrates the effectiveness of the Koopman-BoxQP framework on numerical benchmarks.

Provides a structure-exploited and warm-starting interior-point algorithm for BoxQP.

Abstract

Solving large-scale nonlinear model predictive control (NMPC) problems at kilohertz (kHz) rates on standard processors remains a formidable challenge. This paper proposes a Koopman-BoxQP framework that i) learns a linear Koopman high-dimensional model, ii) eliminates the high-dimensional observables to construct a multi-step prediction model of the states and control inputs, iii) penalizes the multi-step prediction model into the objective, which results in a structured box-constrained quadratic program (BoxQP) whose decision variables include both the system states and control inputs, iv) develops a structure-exploited and warm-starting-supported variant of the feasible Mehrotra's interior-point algorithm for BoxQP. Numerical results demonstrate that Koopman-BoxQP can solve a large-scale NMPC problem with $1040$ variables and $2080$ inequalities at a kHz rate.