A Parametric Multi-Convex Splitting Technique with Application to Real-Time NMPC

TL;DR

This paper introduces a new splitting scheme for parametric multiconvex programs, enabling efficient real-time NMPC solutions with stability guarantees, demonstrated through a bilinear NMPC control of a DC motor.

Contribution

It proposes a novel fixed-iteration splitting method suitable for real-time NMPC and distributed computing, with theoretical stability analysis under semi-algebraic assumptions.

Findings

Method effectively solves bilinear NMPC problems in real-time

Sub-optimality error remains stable with proper parameter tuning

Demonstrated successful control of a DC motor using the proposed approach

Abstract

A novel splitting scheme to solve parametric multiconvex programs is presented. It consists of a fixed number of proximal alternating minimisations and a dual update per time step, which makes it attractive in a real-time Nonlinear Model Predictive Control (NMPC) framework and for distributed computing environments. Assuming that the parametric program is semi-algebraic and that its KKT points are strongly regular, a contraction estimate is derived and it is proven that the sub-optimality error remains stable if two key parameters are tuned properly. Efficacy of the method is demonstrated by solving a bilinear NMPC problem to control a DC motor.